SECOND   YEAR 
COLLEGE   CHEMISTRY- 


BY 

WILLIAM  H.  CHAPIN 
'/ 

ASSOCIATE  PROFESSOR  OF  CHEMISTRY  IN  OBERLJN  COLLEGE 


NEW  YORK 

JOHN  WILEY  &  SONS,  Inc. 

LONDON:  CHAPMAN  &  HALL,  LIMITED 
1922 


Of/ 


Copyright,  1922 

BY 

WILLIAM  H.  CHAPIN 


PRESS  OF 

BRAUNWORTH   &  CO. 

BOOK   MANUFACTURERS 

BROOKLYN,    N.    Y. 


"  When  you  can  measure  what  you  are  speaking  about 
and  express  it  in  numbers,  you  know  something  about  it, 
and  when  you  cannot  measure  it,  when  you  cannot  express 
it  in  numbers,  your  knowledge  is  of  a  meagre  and  un- 
satisfactory kind.  It  may  be  the  beginning  of  knowledge, 
but  you  have  scarcely  in  your  thought  advanced  to  the 
stage  of  a  science." 

LORD  KELVIN. 


484311 


PREFACE 


THE  trend  of  our  present-day  research  in  both  pure  and  applied 
Chemistry  implies  that  principles  are  more  important  than  facts  and 
methods;  and  this  trend,  it  would  seem,  should  be  reflected  in  our 
teaching.  It  is  conceded,  however,  that  general  principles  cannot  be 
profitably  taught  without  first  building  a  background  of  facts,  and  for 
this  reason  the  first  year  course  must  be  largely  given  over  to  descrip- 
tive matter.  It  is  true  that  the  student  has  many  principles  and  laws 
thrust  upon  him  during  the  first  year;  but,  due  to  his  lack  of  perspect- 
ive and  his  crudeness  as  a  manipulator,  he  gets  these  only  in  a  vague, 
qualitative  form.  They  do  not  become  a  part  of  his  stock-in-trade; 
and  so,  after  a  summer's  vacation,  they  have  for  the  most  part  passed 
into  oblivion. 

Now,  if  we  grant  that  these  general  principles  are  the  framework  of  our 
science  we  should  not  allow  them  to  be  thus  forgotten;  we  should  revive 
them,  and  expand  them,  and  work  them  over,  until  they  become  familiar, 
usable  tools.  With  this  in  mind,  therefore,  the  selection  of  courses 
immediately  following  General  Chemistry  is  seen  to  be  a  matter  of  great 
importance.  The  traditional  course  in  Qualitative  Analysis,  with  its 
endless  round  of  reactions  and  "  unknowns,"  offers  very  little  in  the 
development  and  fixing  of  principles,  although  it  has  a  distinct  value 
in  the  first-year  course  as  a  means  of  systematizing  a  multitude  of 
facts.  Even  the  modernized  course  based  on  the  Ionic  Theory  and  the 
Laws  of  Chemical  Equilibrium  makes  too  small  a  contribution  in  pro- 
portion to  the  time  consumed.  The  fact  is  that  too  little  impression 
is  made  on  a  student  by  a  multiplication  of  qualitative  statements  or 
the  use  of  qualitative  problems  and  laboratory  exercises.  What  a 
student  needs  is  an  accurate  restatement  of  principles  and  the  oppor- 
tunity to  verify  and  use  these  in  a  quantitative  way. 

The  course  covered  by  this  text  and  the  accompanying  manual 
is  an  attempt  to  put  into  operation  the  plan  implied  in  the  above  dis- 
cussion. It,  therefore,  assumes  that  the  student  knows  very  little 
about  general  principles  but  that  he  has  a  fair  knowledge  of  facts.  With 
this  slight  assumption,  the  text  takes  up  the  principles  touched  upon 
during  the  first  year,  and  restates  them  without  apology.  After  this 


vi  PREFACE 

it  extends  the  development  beyond  the  possibilities  of  the  first  year, 
and,  wherever  possible,  puts  matters  into  strictly  quantitative  form, 
emphasizing  this  principle  by  the  use  of  quantitative  problems  and 
exercises.  The  laboratory  course  follows  the  same  method;  it  requires 
the  student  to  verify  the  principles  and  to  use  them  in  a  quantitative 
way,  and  thus  make  them  his  own. 

Neither  the  student  nor  the  teacher  is  asked  to  accept  very  much 
on  faith.  Wherever  possible,  statements  are  supported  by  experi- 
mental data,  and  these  are  covered  by  references  to  books  and  original 
papers.  This  tends  to  disarm  much  of  the  skepticism  which  the  begin- 
ner carries  over  from  the  first  year,  and  allows  those  who  are  interested, 
whether  students  or  teacher,  to  extend  the  treatment  of  any  topic 
beyond  the  narrow  limits  of  this  course.  More  than  this,  it  develops 
the  indispensable  habit  of  consulting  the  literature. 

With  many  of  the  most  important  topics,  the  historical  method 
of  treatment  has  been  used.  This  consumes  a  little  more  time,  but 
it  serves  to  introduce  the  student  to  the  pioneers  of  our  science,  and 
attracts  those  who  are  interested  in  the  personal  side.  The  same  end 
is  furthered  by  the  use  of  footnotes  introducing  the  persons  mentioned 
in  the  text,  and  referring  to  books  and  papers  where  further  informa- 
tion may  be  found. 

The  treatment  throughout  the  course  is  intended  to  lead  the  student 
to  feel  that  Chemistry  is  a  growing  science.  To  this  end,  the  author 
often  discusses  questions  which  are  still  unsolved  and  upon  which  work 
is  now  being  done;  and  in  many  cases  also,  the  values  presented  are 
frankly  acknowledged  to  have  only  a  temporary  standing. 

Neither  the  choice  of  topics  nor  the  treatment  of  those  which  have 
been  chosen  will  suit  every  reader.  The  aim  has  been  to  emphasize 
those  principles  which  are  of  fundamental  importance  to  every  chemist 
who  aspires  to  be  something  more  than  an  "  analyst,"  and  to  treat  them 
in  such  a  way  that  the  second-year  student,  with  his  poor  perspective, 
may  constantly  feel  that  he  is  master  of  the  situation.  Moreover, 
the  course  is  not  intended  to  usurp  the  place  held  by  formal  Physical 
Chemistry.  It  is  intended  only  to  place  in  the  student's  hands,  at 
the  earliest  possible  moment,  some  of  the  indispensable  tools  of  the 
science.  It  does  serve,  however,  as  an  introduction  to  Physical  Chem- 
istry, and  it  causes  the  student  to  feel  the  need  of  such  a  course  and 
to  look  upon  it  as  a  logical  and  necessary  step  in  advance. 

The  author  wishes  to  acknowledge  his  great  indebtedness  to  Pro- 
fessor H.  N.  Holmes  of  Oberlin  College,  who  has  taken  the  keenest 
interest  in  the  devolpment  of  this  course  from  its  beginning.  Special 


PREFACE  vii 

mention  should  also  be  made  of  Dr.  W.  V.  Metcalf  of  Oberlin,  Ohio, 
who  as  been  kind  enough  to  read  the  manuscript  and  make  most  val- 
uable suggestions;  also  of  Dr.  A.  P.  Lothrop  of  Queens  College,  Ont., 
who  has  read  the  page  proof. 

WILLIAM  H.  CHAPIN. 


SUGGESTED  COURSE  OF  STUDY 


As  taught  by  the  author,  the  text  is  made  to  cover  a  year's  work 
(thirty-two  weeks,  two  recitations  per  week).  The  ground  is  actually 
covered  in  twenty-eight  weeks,  and  the  last  four  weeks  are  used  in  re- 
views. The  laboratory  manual  can  be  made  to  cover  thirty-two  weeks, 
working  at  the  rate  of  five  hours  per  week;  but  the  author  has  preferred 
to  use  it  in  connection  with  a  course  in  Quantitative  Analysis,  alter- 
nating the  two  kinds  of  work  to  suit  the  work  in  the  classroom.  For 
example,  the  chapters  in  the  text  on  the  Periodic  System,  Atomic  Struc- 
ture, etc.,  cannot  be  illustrated  in  the  laboratory,  and  are  best  accom- 
panied by  gravimetric  analysis,  which  consists  quite  largely  of  tech- 
nique. This  also  gives  a  fine  opportunity  to  apply  the  principles  relating 
to  calculations,  etc.,  previously  studied.  Volumetric  analysis  is  intro- 
duced in  the  second  semester,  while  the  matter  of  equilibrium  is  being 
studied,  and  as  a  fine  illustration  of  such  matters  as  concentration, 
valence,  oxidation,  reduction,  and  indicators,  previously  treated.  This 
combined  analytical  and  theoretical  work  occupies  about  nine  or  ten 
hours  per  week  for  a  year  of  thirty-two  weeks. 

The  actual  division  of  the  time  for  class  and  laboratory  has  been 
about  as  follows: 

First  Semester 

TEXT  LABORATORY 

7  weeks,  through  "  Valence."  7  weeks,  through  "  Valence." 

9  weeks,  through  "  Osmotic  Pressure."         7  weeks,  through  "Gravimetric  Analysis." 

2  weeks,  through  "  Freezing  Points." 


Second  Semester 
TEXT  LABORATORY 


12  weeks,  through  "  Electro-chemistry."       3  weeks,  thjough  "  Indicators." 
4  weeks,  reviews  or  study  of  analytical      7  weeks,  Volumetric  analysis. 

problems  and  principles.  6  weeks,  through  "  Electro-chemistry." 

The  course  as  above  outlined  has  given  the  best  satisfaction,  but 
there  would  be  no  difficulty  in  substituting  a  course  in  advanced 
Qualitative  for  the  Quantitative,  if  it  were  so  desired. 


ix 


TABLE   OF  CONTENTS 


CHAPTER  PAGE 

I.  KINETIC  THEORY v 1 

II.  THE  GAS  LAWS 12 

III.  LAWS  GOVERNING  CHANGE  OF  STATE 25 

IV.  AVOGADRO'S   LAW  AND    MOLECULAR  WEIGHTS 39 

V.  THE  QUANTITATIVE  LAWS  OF  CHEMICAL  COMBINATION 46 

VI.  THE  ATOMIC  HYPOTHESIS  AND  ATOMIC  WEIGHTS 55 

VII.  SYMBOLS,  FORMULAS,  AND  EQUATIONS:   CHEMICAL  CALCULATIONS.  ...     66 

VEIL  CHEMICAL  VALENCE 72 

IX.  CLASSIFICATION  OF  THE  ELEMENTS:  THE  PERIODIC  SYSTEM 88 

X.  RAYS  FROM  VACUUM  TUBES,  RADIOACTIVITY,  ATOMIC  DISINTEGRATION.  106 

XI.  ATOMIC  STRUCTURE  AND  CHEMICAL  COMBINATION 123 

XII.  SOLUBILITY  AND  SUPERSATURATION:  CONCENTRATION 141 

XIII.  FREEZING  POINTS  AND  BOILING  POINTS  OF  SOLUTIONS:  OSMOTIC  PRES- 

SURE: VAN'T  HOFF'S  GENERALIZATION 156 

XIV.  THE  THEORY  OF  IONIZATION 166 

XV.  CHEMICAL  INDICATORS 187 

XVI.  HOMOGENEOUS  EQUILIBRIUM 196 

XVII.  HETEROGENEOUS  EQUILIBRIUM 228 

XVIII.  COMPLEX  EQUILIBRIUM 245 

XIX.  ELECTROCHEMISTRY 263 

APPENDIX 

I.  TABLE  OF  LOGARITHMS 302 

II.  INDEX 305 

III.  TABLE  OF  ATOMIC  WEIGHTS..,  .  .Inside  back  cover 


SECOND  YEAR  CHEMISTRY 


CHAPTER  I 
OUTLINE  OF  THE  KINETIC  THEORY 

MUCH  of  the  material  before  us  deals  with  simple  applications  of 
the  Kinetic  Theory — the  theory  of  moving  molecules.  We  shall,  there- 
fore, begin  by  outlining  the  postulates  of  this  theory,  at  the  same  time 
presenting  some  of  the  experimental  evidence  upon  which  they  are 
based. 

The  Molecular  Structure  of  Matter. — That  matter  is  not  con- 
tinuous, but  is  made  up  of  minute  particles  more  or  less  widely  sepa- 
rated, is  now  accepted  by  every  one  whose  judgment  is  worth  consider- 
ing. Originally  the  idea  of  molecules  rested  on  mere  philosophical 
speculation,  but  in  modern  times  quantitative  evidence  has  accumu- 
lated, until  scientists  the  world  over  now  feel  that  the  theory  is  not 
even  open  to  question:  it  is  accepted  as  a  demonstrated  fact. 

This  does  not  mean  that  we  can  see  molecules,  or  ever  hope  to  do 
so,  for  the  limitations  of  our  organs  of  vision  make  this  forever  impos- 
sible. "  But,"  as  Professor  Millikan  *  says,  "  after  all,  the  evidence 
of  our  eyes  is  about  the  least  reliable  kind  of  evidence  which  we  have. 
We  are  continually  seeing  things  which  do  not  exist,  even  though  our 
habits  are  unimpeachable.  It  is  the  relations  which  are  seen  by  the 
mind's  eye  to  be  the  logical  consequences  of  exact  measurement  which 
are  for  the  most  part  dependable."  If  we  cannot  see  molecules  we 
can,  nevertheless,  make  all  sorts  of  exact  and  reliable  measurements 
relating  to  them,  and  can  successfully  predict  their  deportment  under 
any  given  conditions.  This  is  better  than  seeing. 

As  to  the  matter  of  evidence  upon  which  the  conception  of  mole- 
cules rests  we  shall  say  very  little  here.  The  volume  of  this  evidence 

*  Robert  Andrews  Millikan  (1868-  ),  Chairman  of  the  Executive  Committee 
and  Director  of  Physical  Research,  California  Institute  of  Technology.  Noted  for 
his  magnificent  work  on  the  determination  of  the  electronic  charge. 


2 


.-OUTLINE-  QF'THE  KINETIC  THEORY 


is  enormous,  for  practically  all  the  physical  deportment  of  matter  in 
all  its  states  can  be  explained  on  no  other  basis.  We  therefore  prefer 
to  let  the  evidence  appear  and  accumulate  as  we  proceed.  We  might, 
however,  mention  one  or  two  striking  cases  in  passing.  We  note,  for 
example,  the  enormous  compressibility  of  gases.  We  cannot  con- 
ceive how  matter  can  be  made  to  occupy  a  smaller  space  if  it  already 
occupies  it  all.  There  must  be  free  space;  and  admitting  this  is 
equivalent  to  admitting  that  gases  have  a  discontinuous  structure. 
The  manner  in  which  one  substance  dissolves  in  another  and  diffuses 
about  in  it  is  another  convincing  piece  of  evidence.  But  perhaps  the 
best  evidence  is  the  fact  that  certain  properties  of  matter  change  sud- 
denly in  a  very  striking  way  when  the  dimensions  pass  a  certain  limit 
of  smallness.  It  is  known,  for  example,  that  a  particle  of  camphor 
gum  placed  upon  the  surface  of  pure  water,  is  made  to  skip  or  whirl 
about  by  changes  of  surface  tension.  Now,  Lord  Rayleigh  *  found 
that  this  action  was  stopped  when  a  film  of  oil  10X10~8  cm.  in  thick- 
ness was  formed  upon  the  water,  while  a  film  of  8X10~8  cm.  had  no 
effect.  This  difference  was  due,  he  said,  to  the  fact  that  in  the  first 
case  the  water  was  covered  over  with  a  film  of  liquid  oil,  while  in  the 
second  case  only  individual  molecules  were  dotted  about,  leaving 
exposed  surfaces  of  water  between. 

We  may  note  in  passing  that  the  methods  employed  in  molecular 
measurement  are  largely  statistical  in  nature.  We  predict  the  happen- 
ings and  conditions  in  a  world  of  molecules  just  as  we  predict  matters 
having  to  do  with  human  society.  An  insurance  company,  for  example, 
can  predict  with  considerable  accuracy  the  number  of  people  who  will 
be  killed  in  automobile  accidents  during  a  year,  or  can  give  the  exact 
weight  of  the  average  American  man  or  woman  of  a  given  age.  Con- 
cerning a  single  individual  they  can  tell  very  little,  but  the  larger  the 
number  of  individuals  the  more  accurate  the  prediction  will  be.  In 
the  molecular  world,  where  the  number  of  individuals  is  extremely 
large,  the  predictions  and  averages  are  very  exact.  To  quote  Pro- 
fessor Millikan  again:  "  We  can  estimate  the  number  of  molecules  in 
a  cubic  centimeter  of  gas  with  greater  precision  than  we  can  attain  in 
determining  the  number  of  people  living  in  New  York."  In  the  same 
way  we  can  probably  determine  the  mass  of  a  molecule  of  oxygen  much 
more  accurately  than  we  can  determine  the  average  weight  of  an  Ameri- 
can Indian. 

We  shall  now  proceed  to  describe  certain  molecular  properties  and 

*  Phil.  Mag.  (5)  30,  474  (1890)  .  [Lord  Rayleigh  (1842-  ).  One  of  the  world's 
most  brilliant  physicists.  Co-discoverer  of  the  rare  gases  in  the  atmosphere.] 


MOTION  AND  KINETIC  ENERGY  OF  MOLECULES  3 

dimensions  and  to  show  in  a  very  elementary  way  how  some  of  these 
matters  have  been  found  out. 

Motion  and  Kinetic  Energy  of  Molecules. — Molecules  are  in  rapid 
motion  and  their  kinetic  energy  is  proportional  to  the  absolute  temper- 
ature. 

Pressure,  in  the  case  of  gases,  we  believe  to  be  due  to  the  impacts 
of  vibrating  molecules;  and  the  fact  that  gases  do  not  settle  down 
like  dust  can  be  accounted  for  only  on  the  supposition  that  the  mole- 
cules are  constantly  moving  and  stirring  each  other  up. 

What  we  call  heat  we  also  believe  to  be  due  to  the  energy  of  motion 
(the  kinetic  energy  *)  of  moving  molecules,  f  When  we  touch  a  body 
whose  molecules  are  in  very  rapid  motion  the  motion  is  imparted  to 
the  molecules  of  the  hand,  and  we  sense  the  effect  as  what  we  call 
"  heat."  An  object  expands  as  heat  is  applied  because  the  moving 
molecules,  as  their  rate  of  vibration  increases,  jostle  each  other  apart. 

But  the  motion  and  kinetic  energy  of  molecules  are  shown  most 
convincingly  by  what  is  called  Brownian  movement.  If  a  very  fine 
powder  suspended  in  water  is  examined  under  a  good  microscope  the 
particles  are  seen  to  be  in  rapid  vibration — the  smaller  the  particles 
the  more  rapid  the  vibration.  This  motion  has  been  named  Brownian 
movement  after  its  discoverer,  Robert  Brown,  a  botanist.  It  has 
been  very  carefully  studied  by  Perrin  J  and  others,  and  these  investi- 
gators have  come  to  the  very  important  conclusion  that  what  we  see 
is  only  an  example  of  what  is  going  on  all  the  way  down  from  the  largest 
particles  through  all  grades  of  smallness  to  the  molecules  themselves. 
They  believe  thai  all  the  particles  of  every  size,  whether  visible  or 
invisible,  have  by  their  mutual  impacts  imparted  their  kinetic  energy 
to  each  other  until,  on  the  average,  they  all  have  the  same  amount. § 
The  difference  in  the  rate  of  movement  is  due  to  the  fact  that  to  have 
the  same  kinetic  energy  the  large  particles  need  only  move  slowly, 
while  the  smaller  particles  must  move  more  rapidly,  and  the  smallest 
particles  most  rapidly.  That  this  supposition  is  correct  has  been  proved 
experimentally  for  the  visible  particles,  and  the  smallest  of  these  is 
not  far  removed  in  size  from  the  largest  molecules.  It  is,  therefore, 

*  The  kinetic  energy  of  any  moving  object  is  related  to  the  mass  and  speed,  as 
shown  in  the  common  kinetic  expression:  K.E.=Af>S2/2.  The  derivation  of  this 
expression  may  be  found  in  any  text-book  of  physics,  e.g.,  Millikan  and  Gale,  p.  151. 
Note  that  kinetic  energy  varies  as  the  square  of  the  speed.  This  means  that  the 
kinetic  energy  of  an  object  will  be  quadrupled  when  the  speed  is  doubled. 

t  Or  of  the  smaller  particles  constituting  the  molecules. 

J  "  Brownian  Movement  and  Molecular  Reality,"  and  "  Atoms."  [Jean  Perrin 
(1870-  ),  Professor  of  Physical  Chemistry  at  the  Sorbonne,  Paris.] 

§  This  is  called  the  Law  of  Equipartition  of  Energy. 


4  OUTLINE  OF  THE  KINETIC  THEORY 

not  a  serious  stretch  of  the  imagination  to  believe  that  the  slightly 
smaller  particles — the  molecules — act  in  the  same  way  and  have  the 
same  amount  of  kinetic  energy. 

That  the  kinetic  energy  is  proportional  to  the  absolute  temperatures 
has  been  demonstrated  in  the  case  of  the  visible  particles,  and  that  the 
same  thing  is  true  for  the  molecules,  is  evidenced  by  the  fact  that  gase- 
ous pressure  is  proportional  to  the  absolute  temperature.  Pressure  is, 
of  course,  a  measure  of  kinetic  energy,  and  if  pressure  is  proportional 
to  the  temperature,  the  kinetic  energy  must  also  be  proportional  to 
the  temperature. 

It  may  be  interesting  to  include  here  some  of  the  actual  speeds  which 
molecules  possess.*  The  average  speed  of  the  hydrogen  molecule 
between  impacts  with  other  molecules  is,  under  standard  conditions, 
183,000  cm.  (1.15  miles)  per  second.  That  of  the  oxygen  molecule 
is  46,000  cm.  per  second.  It  is  to  be  carefully  noted  that  we  say 
"  average  speed."  f  It  is  not  to  be  expected  that  all  the  molecules, 
or  any  one  individual,  will  necessarily  be  moving  at  this  speed;  but 
the  average  speed  for  many  millions  of  molecules  will  certainly  come 
very  near  these  values.  Particular  individuals  will  be  moving  at  every 
conceivable  speed,  some  above,  some  below  this  average.  The  method 
by  which  these  average  speeds  are  calculated  will  be  described 
later. 

Elasticity  of  Molecules. — Molecules  must  be  perfectly  elastic.  By 
this  we  mean  that  if  two  molecules  collide  and  rebound  no  kinetic 
energy  is  lost. 

When  a  given  quantity  of  a  gas  is  allowed  to  stand  under  constant 
conditions  the  pressure  remains  perfectly  constant.  As  before  stated, 
pressure  is  undoubtedly  due  to  molecular  impact.  If  the  pressure 
remains  constant  it  must  be  that  the  average  speed  of  the  molecules 
also  remains  constant,  and  this  could  not  be  so  if  the  molecules  were 
not  perfectly  elastic.  If  the  molecules  were  like  balls  of  putty,  or  even 
balls  of  lead,  they  would  rebound  after  impact  with  constantly  lessened 
speed  until  they  finally  came  to  rest.  The  pressure  would,  therefore, 
decrease  correspondingly  until  it  became  zero. 

Number  and  Spacing  of  the  Molecules  of  a  Gas. — The  number  of 
molecules  of  gas  per  liter  under  standard  conditions  is  known  with  con- 
siderable accuracy.  As  determined  by  several  reliable  methods  the 
number  is  about  2.7X1022.  The  remarkable  thing  is  that,  although 
the  methods  of  measurement  are  very  different,  the  results  are  so 

*  First  calculated  by  Joule,  the  English  Physicist,  in  1851.  See  Phil.  Mag., 
XIV,  211. 

f  Nernst,  Theoretical  Chemistry,  pp.  434-437,  (1911).    Other  references  are  given. 


NUMBER  OF  SPACING  OF  THE  MOLECULES  OF  A  GAS  5 

nearly  the  same.  This  is  a  good  argument  in  favor  of  their  accu- 
racy. One  of  the  methods  of  determining  this  number  involves  an 
actual  count  of  the  number  of  particles  seen  in  Brownian  movement. 
Perrin  *  made  the  determination  in  this  way.  He  prepared  sus- 
pensions of  mastic  or  gamboge  particles  of  uniform  size  and  examined 
them  under  the  microscope  in  a  tiny  cell  0.1  mm.  deep.  Pressure  due 
to  their  kinetic  energy  tends  to  make  the  particles  scatter  and  become 
equally  distributed  through  the  cell.  Gravity  pulls  them  towards  the 
bottom,  bringing  them  closer  together  there,  When  equilibrium  is 


FIG.  1. — Distribution  of  Gamboge  Particles  under  the   Influence  of   Gravitation 
with  Micrographs  Taken  at  Different  Depths. 

established  these  two  tendencies  balance.  Perrin  counted  the  number 
present  at  different  levels  (a,  6,  c)  equal  distances  apart,  as  seen  in  the 
fields  a' ',  b',  and  c',  and  from  the  rate  of  increase  in  the  concentration 
was  able  to  calculate  the  number  required  in  unit  volume  to  give  a 
pressure  of  one  atmosphere  (760  mm.)  at  0°  C.  He  varied  the  size 
of  the  particles  fifty-fold,  and  always  found  nearly  the  same  number 
(as  above).  He  therefore  inferred  that  the  number  would  be  the  same 
even  for  gaseous  molecules.  This  means  that  a  liter  of  any  gas  under 
given  conditions  of  temperature  and  pressure  will  contain  the  same 
number  of  molecules,  no  matter  what  their  size  may  be.  This  fact 


*  "  Atoms,"  pp.  83-108. 


6  OUTLINE  OF  THE  KINETIC  THEORY 

was  suspected  by  the  Italian  physicist,  Avogadro,*  long  before  the 
kinetic  theory  was  developed,  and  is  known  as  Avogadro's  Law. 

Considering  the  number  of  molecules  per  liter,  we  can  see  that  the 
spacing  of  the  molecules  of  a  gas  under  standard  conditions  must  be 
very  close  if  measured  in  the  relatively  coarse  units  of  centimeters  or 
inches.  But  relative  to  their  own  size  the  molecules  of  a  gas  are  really 
quite  far  apart.  That  this  is  true  is  shown  by  the  wonderful  compress- 
ibility of  gases.  Thus  one  liter  of  carbon  dioxide  gas  at  0°  C.  and  one 
atmosphere  pressure  can  be  compressed  until  it  changes  into  a  liquid 
which  occupies  only  2  cc.  If  we  assume  that  the  volume  of  the  liquid 
represents  the  total  volume  of  the  molecules,  the  free  space  between 
the  molecules  of  one  liter  of  the  gas  is  998  cc.,  or  449  times  the  volume 
occupied  by  the  molecules  themselves.  One  liter  of  steam  at  100°  C. 
and  one  atmosphere  pressure  can  be  compressed  to  water  which  occu- 
pies 0.6  cc.  In  this  case,  therefore,  the  free  space  in  one  liter  of  gaseous 
water  must  have  been  at  least  999.4  cc. 

The  actual  spacing  of  the  molecules  may  be  calculated  with  fair 
accuracy  from  the  number  per  cubic  centimeter.  Thus  1  cc.  contains 
2.7X1019  molecules.  Taking  the  cube  root  of  this  we  have  the  number 
in  one  linear  centimeter.  This  number  is  3X106.  The  distance  apart 
from  center  to  center  averages,  therefore,  3.3X10"7  cm.  (  =  0.00000033 
cm.).  It  must  be  noted  that  this  is  the  average  spacing.  The  actual 
distance  apart  of  contiguous  individuals  will,  of  course,  vary  widely, 
and  will  be  constantly  changing. 

Size  of  Molecules. — Molecules  vary  considerably  in  size,  depend- 
ing on  the  substance  from  which  they  come.  This  we  should,  of  course, 
expect.  And  yet  the  variation  is  not  so  great  as  one  might  expect  it 
to  be.  The  fact  is  that  molecules  must  be  regarded  as  complex  systems, 
and  not  at  all  like  smooth  balls,  as  we  sometimes  erroneously  imagine. 
To  speak  about  the  size  of  a  molecule  is  somewhat  like  speaking  about 
the  size  of  our  solar  system.  We  might  consider  it  as  extending  to  the 
orbit  of  Neptune,  for  example,  but  the  sphere  of  influence  of  our  sun 
certainly  extends  farther  than  this.  So  the  size  of  molecules  is  prob- 
ably not  a  very  definite  thing,  and  is  probably  a  question  of  how  far 
the  sphere  of  influence  extends  in  each  case.  Hence  we  are  not  very 
much  surprised  to  find  that,  so  far  as  we  can  measure,  the  hydrogen 
molecule  does  not  differ  very  largely  in  size  from  the  water  molecule 
or  even  from  others  which  we  might  expect  to  be  much  larger.  We 
may  include  here  one  method  of  calculating  at  least  the  approximate 

*  Amadeo  Avogadro  (1776-1856),  Professor  of  Physics  at  the  University  of 
Turin.  No  physical  law  ever  discovered  is  more  fundamental  and  far-reaching 
than  Avogadro's  Law. 


MEAN  FREE  PATH  OF  GASES  7 

size  of  molecules.  In  speaking  about  the  spacing  of  molecules  we 
showed  that  one  liter  of  carbon  dioxide  gas  under  standard  conditions 
could  be  condensed  to  a  liquid  occupying  2  cc.  If  we  call  2  cc.  the  total 
volume  of  all  the  molecules  in  one  liter  and  divide  this  by  the  number 
of  molecules  in  one  liter  (2.7X1022)  we  shall  have  the  volume  occupied 
by  one  molecule  of  CO2.  We  find  this  to  be  7X10~23  cc.  The  volume 
of  one  water  molecule,  calculated  in  the  same  way,  is  3.03  X10~23  cc. 
One  liter  of  hydrogen  gas  under  standard  conditions  gives,  when  con- 
densed, 1.3  cc.  of  liquid  hydrogen.  Dividing  this  by  the  number  of  mole- 
cules per  liter,  as  above,  we  obtain  for  the  volume  of  one  hydrogen 
molecule  4.8  X  10~23  cc.  All  these  calculations  are  based  on  the  assump- 
tion that  the  space  occupied  by  the  liquid  is  equivalent  to  the  com- 
bined volume  of  all  the  molecules,  and  this  may  not  be  quite  true; 
but  the  values  obtained  in  this  way  are  not  far  from  those  calculated 
in  other  ways,  and  so  are  probably  not  greatly  in  error.  They  show 
conclusively  that  molecules  of  different  substances  do  not  necessarily 
vary  widely  in  size  even  when  they  do  vary  in  mass. 

We  should  note  here  that  all  calculations  lead  inevitably  to  the  con- 
clusion that  the  molecules  of  any  one  kind  are  of  the  same  size  and  mass. 
Thus,  if  some  of  the  molecules  of  a  gas  were  larger  and  heavier  than 
the  rest  they  would  move  at  a  slower  speed.  If  such  a  gas  were  made 
to  pass  through  a  porous  partition  the  small,  speedy  molecules  would 
get  through  first,  and  we  should  thus  be  able  to  separate  the  gas  into 
varieties  having  different  physical  properties.  This  has  never  been 
done,  and  we  therefore  conclude  that  the  molecules  of  any  one  kind 
are  exactly  alike.* 

Mean  Free  Path  in  Gases. — One  of  the  most  important  points 
connected  with  the  theory  of  gases  is  the  matter  of  the  average  dis- 
tance over  which  the  molecules  travel  between  collisions.  This  is 
called  the  "  mean  free  path."  It  is  not  to  be  confused  with  the  aver- 
age spacing  mentioned  above,  for  a  molecule  may  travel  several  times 
the  average  spacing  distance  before  colliding  with  another  molecule. 
As  calculated  by  several  reliable  methods,  the  mean  free  path  for  any 
gas  under  standard  conditions  is  not  far  from  0.00001  cm.f  If  the 

*  Some  very  recent  work  by  W.  D.  Harkins  seems  to  indicate  that  ordinary 
chlorine  gas  may  possibly  be  separated  by  diffusion  into  two  isotopic  forms  having 
the  same  chemical  properties  but  different  molecular  weights.  This  fact  does  not, 
however,  refute  the  statement  made  above,  for  the  two  forms  of  chlorine  cannot  be 
regarded  as  quite  the  same  substance.  Harkins'  paper  appears  in  Science,  Mar.  19, 
1920,  page  289. 

f  This  value  was  first  calculated  by  Clerk-Maxwell,  the  noted  English  physicist, 
1860.  See  Phil.  Mag.  (1860;  4th  series),  28.  See  also,  O.  E.  Meyer,  Kinetic  Theory 
of  Gases. 


8  OUTLINE  OF  THE  KINETIC  THEORY 

average  spacing  is  0.00000033  cm.,  it  follows  that  a  molecule  passes 
about  thirty  of  its  neighbors  before  it  finally  collides  with  one;  that  is, 
the  mean  free  path  is  about  thirty  times  the  average  spacing. 

The  matter  of  mean  free  path  carries  with  it  some  important  con- 
sequences. In  the  case  of  a  gas  at  ordinary  pressure  where  the  mean 
free  path  is  only  0.00001  cm.,  it  is  evident  that  the  molecules,  in  dif- 
fusing over  a  distance  of  a  few  centimeters,  would  have  to  travel  over 
a  very  intricate  zigzag  path.  Such  diffusion  would  then  be,  in  general, 
a  rather  slow  process.  If,  however,  the  pressure  of  the  gas  were  lowered 
to  say  1  mm.  the  mean  free  path  would  be  several  hundred  times  as 
great,  and,  other  things  being  equal,  the  rate  of  diffusion  should  be  very 
much  increased.  This  is  nicely  shown  by  the  great  increase  in  the  speed 
with  which  a  liquid  evaporates  in  a  vacuum  desiccator.  The  mole- 
cules must  diffuse  between  the  molecules  of  the  air  to  get  away  from 
the  surface  of  the  liquid,  and  since  the  number  of  these  air  molecules 
is  made  small  the  rate  of  diffusion  is  greatly  increased. 

Another  matter  which  is  dependent  on  the  mean  free  path  is  the 
passage  of  electricity  through  gases.  The  only  way  gases  can  conduct 
electricity  is  by  the  process  of  convection.  Certain  molecules  touch 
one  of  the  electrodes  and  become  charged.  This  charge  they  then 
carry  by  the  process  of  diffusion  to  the  opposite  electrode.  With 
gases  at  atmospheric  pressure,  the  process,  due  to  the  short  free  path, 
is  almost  infinitely  slow.  They  practically  do  not  conduct  at  all.  But 
in  the  so-called  vacuum  tubes  where  the  mean  free  path  is  very  much 
greater,  conduction  takes  place  with  considerable  readiness. 

The  Mutual  Attraction  of  Molecules. — What  we  have  said  thus 
far  might  lead  to  the  supposition  that  molecules  always  act  as  perfectly 
independent  individuals.  It  is  well  known,  however,  that  this  is  not 
the  case.  When  a  gas  is  dilute,  that  is,  when  the  pressure  is  low,  the 
molecules  are  so  widely  separated  that  they  are  for  the  most  part  out- 
side each  other's  spheres  of  influence;  but  at  high  pressures  when  the 
molecules  are  brought  close  together,  the  attraction  at  once  makes 
itself  felt.  This  is  seen  in  the  fact  that  gases  under  high  pressure 
depart  widely  from  the  ordinary  gas  laws — those  of  Boyle  and  Charles. 
In  the  liquid  and  solid  states  also,  we  can  see  at  once  that  the  mole- 
cules really  exert  an  enormous  pull  upon  each  other.  We  know,  for 
example,  how  much  heat  energy  is  required  to  vaporize  a  liquid,  a  proc- 
ess which  acts  against  the  molecular  attraction.  We  shall  often  have 
occasion  to  consider  this  matter  of  attraction — a  matter  which  was  not 
taken  into  account  in  the  early  work  on  gases. 

Structure  and  Kinetic  Properties  of  Liquids. — Our  discussion  thus 
far  has  referred  mainly  to  gases,  and  most  of  this  applies  equally  well 


STRUCTURE  AND  KINETIC  PROPERTIES  OF  LIQUIDS  9 

to  liquids.  Liquids,  however,  possess  some  special  characteristics  which 
need  explanation.  The  distinguishing  property  of  gases  is  their  tend- 
ency to  expand  indefinitely  and  fill  completely  any  container,  no  matter 
how  large.  This  is,  no  doubt,  due  to  the  great  preponderance  of  the 
kinetic  energy  factor  over  that  of  attraction.  Liquids  differ  at  this  point 
for  they  are  bounded  by  a  definite  surface,  and  do  not  tend  to  expand 
indefinitely.  This  we  explain  by  assuming  that  in  liquids  the  attractive 
influence  preponderates:  However,  even  these  differences  are  not 
fundamental,  but  are  simply  matters  of  degree  governed  mainly  by 
temperature  and  pressure  relations.  At  the  critical  point  we  find  these 
differences  vanishing  and  the  two  states  becoming  identical. 

Just  what  we  should  include  under  the  term  "  liquid  "  is  somewhat 
a  matter  of  opinion,  for  the  dividing  line  between  liquid  and  solid  is 
a  rather  indefinite  one.  Possibly  the  real  criterion  of  a  liquid  should 
be  the  ability  to  flow.  If  so,  we  must  include  as  liquids  such  substances 
as  sealing  wax  and  glass,  which  are  popularly  classed  as  solids,  for  these 
substances  do  slowly  flow  and  adapt  themselves  to  new  shapes.  Thus, 
a  rod  of  wax  or  glass  supported  horizontally  by  one  end  will  be 
found  after  the  lapse  of  some  months  to  have  become  permamently 
bent. 

The  matter  of  molecular  attraction,  mentioned  above  as  causing 
a  liquid  to  confine  itself  to  a  definite  volume,  is  also  responsible  for  some 
other  important  properties  of  liquids.  We  know,  for  example,  that 
in  the  case  of  gases  the  closer  the  packing  of  the  molecules  the  greater 
the  pressure.  Considering,  then,  the  extremely  close  packing  of  liquid 
molecules,  liquids  should  exert  enormous  pressures  on  the  walls  of  their 
containers.  But  they  do  not  do  this,  and  we  can  explain  the  fact  only 
by  supposing  that  the  outward  push  of  the  molecules  is  neutralized  by 
their  strong  counter  attraction.  Internal  attraction  takes  part  also 
in  the  condition  seen  at  the  surface  of  liquids  in  what  is  called  "  surface 
tension."  The  molecules  inside  the  liquid  are  attracted  in  every  pos- 
sible direction  by  their  neighbors,  while  those  at  the  surface  are  attracted 
only  inward  and  towards  each  other.  This  makes  the  surface  layer 
dense  and  hard  to  penetrate — somewhat  like  an  elastic  skin  drawn  all 
about  the  liquid.  This  surface  tension  is  illustrated  in  the  toughness 
of  the  soap  bubble  or  the  way  in  which  water  insects  are  supported  on 
the  surface  of  water. 

In  the  matter  of  structure  liquids  do  not  ordinarily  differ  largely 
from  gases.  In  either  case  the  unit  is  the  individual  molecule.  But 
liquids  are  known  which  do  show  a  fundamental  difference.  We  refer 
to  liquids  in  which  some  of  the  molecules  are  united  in  small  aggregates. 
Water,  alcohol,  and  acetic  acid  are  examples  of  this  kind.  Such  liquids 


10  OUTLINE  OF  THE  KINETIC  THEORY 

are  said  to  be  "associated."  *  Cases  are  also  known  in  which  the  mole- 
cules show  an  orderly  arrangement,  such  as  is  seen  in  crystals.  Aggre- 
gates of  this  kind  are  called  "  liquid  crystals."! 

As  to  the  closeness  with  which  liquid  molecules  are  packed  there 
seems  to  be  somewhat  contrary  evidence.  Reasoning  from  compress- 
ibility data,  T.  W.  Richards  |  believes  that  the  molecules  are  in  actual 
contact,  and  that  any  further  compression  means  a  denting  or  defor- 
mation of  the  molecules  themselves.  Bingham,§  on  the  other  hand,  pre- 
sents viscosity  data  to  show  that  liquids  contain  free  space  between 
the  molecules.  If  it  is  remembered,  however,  that  molecules  are 
complex  structures  with  rather  indefinite  boundaries,  the  two  ideas 
may  not  seem  so  divergent.  One  probably  regards  molecules  as  touch- 
ing when  the  volume  they  occupy  includes  something  like  a  maximum 
sphere  of  influence;  the  other  when  the  volume  includes  a  minimum 
sphere  of  influence. 

The  Structure  of  Crystals. — The  structure  of  crystalline  solids  has 
been  a  much-studied  subject.  Not  until  recently,  however,  has  the 
problem  come  anywhere  near  solution.  Spectra  obtained  by  diffraction 
of  X-rays  from  crystal  faces  have  cleared  up  the  mystery,  and  have 
made  it  possible  to  determine  the  exact  structure  in  many  cases.  If 
The  remarkable  part  of  it  all  is  that  in  the  crystal  the  individuality  of 
the  molecule  seems  practically  to  have  vanished  and  the  atom  seems 
to  have  become  the  unit  of  structure.  This  means  that  the  whole 
crystal  is  only  an  extension  of  the  architectural  arrangement  found 
in  the  molecule.  For  example,  the  cubical  crystal  of  potassium  chlo- 
ride is  made  up,  not  of  a  succession  of  independent  molecules  of  KC1, 
but  of  a  rectangular  lattice-work  of  alternate  K  and  Cl  atoms  placed  at 
equal  distances  from  one  another.  Another  remarkable  thing  is  the 
fact  that  other  crystals  of  identical  form  and  of  analogous  composition 
do  not  necessarily  have  the  same  structure.  Thus  the  potassium 
bromide  crystal  has  atoms  not  only  at  the  corners  of  the  simple  cubical 
lattice- work  but  also  at  the  centers  of  the  cube  faces.  Sodium  chloride 
has  an  even  more  complex  structure. 

*  See  Walker,  Physical  Chemistry,  topic,  "  Molecular  Complexity." 

f  Lehman,   Die  neue  Welt  der  Fliissige  Kristalle. 

J  "  Faraday  Lecture,"  Jour.  Chem.  Soc.,  99,  1201.  See  also  Jcur.  Am.  Chem. 
Soc.,  36,  2417.  [Theodore  William  Richards  (1868-  ),  Professor  of  Chemistry, 
Harvard  University.  Noted  for  his  exceedingly  accurate  work  on  atomic  weights 
and  compressibility  of  atoms.  See  Harrow,  Eminent  Chemists  of  our  Time,  p.  59.] 

§Jour.  Am.  Chem.  Soc.,  36,  1393,  (1914).  [Eugene  C.  Bingham  (1878-  ), 
Professor  of  Chemistry,  Lafayette  College.  Noted  for  his  work  on  viscosity  and 
plastic  flow.] 

H  Bragg,  W.  H.,  and  W.  L.,  X-Ray  and  Crystal  Structure. 


EXERCISES  11 


EXERCISES 

1.  Give  evidence  of  the  molecular  structure  of  matter.     How  sure  are  we  that 
molecules  exist? 

2.  Show  how  pressure  and  heat  are  evidences  of  molecular  motion. 

3.  How  is  heat  communicated  from  one  object  to  another? 

4.  Define  kinetic  energy.     How  related  to  heat  and  pressure? 

6.  What  is  Brownian  movement?     What  has  the  study  of  Brownian  movement 
shown  concerning  the  kinetic  energy  of  different-sized  particles  in  the  same  system? 

6.  Gamboge  particles  suspended  in  water  are  seen   to  be  in  rapid  vibration. 
The  average  mass  of  these  particles  is  3600  times  that  of  the  water  molecules.     What 
must  be  the  relative  speed  of  the  gamboge  particles  and  the  water  molecules  that  they 
may  have  the  same  amount  of  kinetic  energy? 

7.  Show  that  the  kinetic  energy  of  molecules  is  proportional  to  the  absolute 
temperature. 

8.  Give  the  actual  average  speeds  of  hydrogen  and  oxygen  molecules  under  stand- 
ard conditions.     Why  say  average  speeds? 

9.  Why  do  we  believe  that  molecules  are  perfectly  elastic? 

10.  What  is  the  number  of  molecules  in  a  liter  of  any  gas  under  standard  con- 
ditions?    How  determined? 

11.  Calculate  the  average  spacing  of  the  molecules  of  a  gas  under  standard  con- 
ditions. 

12.  Calculate  the  amount  of  free  space  in  1  liter  of  CO2  at  0°  and  760  mm.  pres- 
sure; in  1  liter  of  steam  at  100°  and  760  mm. 

13.  Calculate  the  volume  occupied  by  one  molecule  of  CO2;  one  molecule  of 
H2;  one  molecule  of  water.     How  does  the  volume  occupied  by  the  molecule  com- 
pare with  the  average  spacing? 

14.  How  definite  can  we  consider  the  size  of  molecules  to  be? 

15.  Give  evidence  as  to  the  uniformity  in  the  size  of  molecules  of  any  one  kind. 

16.  What  is  meant  by  "  mean  free  path."     What  is  the  average  mean  free  path 
in  a  gas  at  atmospheric  pressure  and  temperature?     How  does  this  compare  with 
the  average  spacing?     Explain. 

17.  Explain  the  rapid  evaporation  of  a  liquid  in  a  "  vacuum  "  desiccator. 

18.  How  do  gases  conduct  electricity?     Why  do  they  conduct  better  under  low 
pressure? 

19.  Give  evidence  of  intermolecular  attraction. 

20.  Why  does  a  liquid  not  exert  a  great  pressure  upon  the  walls  of  its  container? 

21.  Is  glass  a  liquid,  or  a  solid?     Evidence? 

22.  Explain  surface  tension.     Examples. 

23.  What  is  meant  by  "  association  "  and  "  liquid  crystals  "  ? 

24.  Do  the  molecules  of  a  liquid  touch?     Evidence? 

25.  How  has  the  structure  of  certain  crystals  been  determined?     What  is  the 
unit  of  structure?     Give  structure  of  KC1  and  KBr. 


CHAPTER  II 
THE  GAS  LAWS 

Simple  Form  of  Boyle's  Law. — We  have  already  explained  that 
gas  pressure  is  due  to  the  constant  bombardment  of  the  walls  of  the 
container  by  the  rapidly  moving  molecules.  The  intensity  of  gas 
pressure  depends  on  the  number  of  impacts  per  second  and  upon  the 
average  kinetic  energy  of  the  molecules.  Assume  for  the  moment 
that  the  latter  factor  remains  unchanged;  in  other  words,  assume  that 
the  temperature  is  constant.  If,  then,  a  given  quantity  of  gas  is  com- 
pressed until  its  volume  is  reduced  to  one-half  its  original  volume  there 
will  be  twice  as  many  molecules  per  cubic  centimeter  and  consequently 
twice  as  many  impacts  per  second.  This  would  make  the  pressure 
twice  as  great.  Thus  2  gm.  of  hydrogen  at  0°  C.,  occupying  22.4  liters, 
exerts  a  pressure  of  one  atmosphere.  If  the  volume  is  made  11.2  liters 
the  pressure  becomes  two  atmospheres.  Notice  that  the  ratio  here  is 
inverse;  that  is,  when  the  volume  becomes  less  the  pressure  becomes 
greater  in  the  same  proportion.  Notice  also  that  the  product  of  the 
volume  and  the  pressure  is  a  constant  (22.4).  Mathematically  this 
relation  may  be  stated  thus: 

PV  =  K,     or     PV=P'V 

This  is  Boyle's  Law  *  in  its  simplest  form. 

Deviations  from  Boyle's  Law. — For  most  ordinary  gases  at  low 
pressure  this  simple  form  of  Boyle's  law  states  the  facts  very  accu- 
rately. If  gases  were  ideal,  that  is,  if  the  molecules  were  mere  points 
in  space  and  did  not  exert  any  attractive  influence  on  each  other,  it 
would  state  the  facts  for  all  pressures.  But  gases  are  not  ideal  in  these 
respects;  for,  as  we  have  shown,  the  molecules  do  occupy  space  and 
do  attract  each  other.  What,  then,  will  be  the  effect  of  these  two 
influences  on  the  phenomena  included  under  Boyle's  law? 

The  pressure  of  a  gas  depends  on  the  number  of  impacts  made 
by  the  molecules  on  unit  surface  in  unit  time,  and  this  in  turn  depends 

*  Named  for  Robert  Boyle  (1627-1691),  one  of  the  founders  of  the  Royal  Society, 
London. 

12 


DEVIATIONS  FROM  BOYLE'S  LAW  13 

on  the  amount  of  free  space  in  which  the  molecules  move  about.  If 
the  molecules  are  widely  separated,  as  they  are  at  low  pressures,  the 
space  they  actually  occupy  is  nearly  negligible  compared  with  the  total 
volume  of  the  container.  In  this  case  the  free-space  (free  volume) 
and  the  total  volume  are  practically  identical.  We  compress  such 
a  gas  to  half  its  volume,  and  if  the  space  occupied  by  the  molecules  is 
still  nearly  negligible  we  have  simply  doubled  the  number  of  impacts 
upon  unit  surface  and  have  thus  doubled  what  we  call  the  pressure. 
Such  a  gas  is  "  obeying  "  Boyle's  law  very  closely.  Suppose,  on  the 
other  hand,  we  have  a  gas  under  such  pressure  that  the  molecules  occupy 
one-tenth  of  the  total  volume  of  the  container.  The  free  volume  is 
now  10—  1,  or  9.  If  we  compress  this  gas  so  that  the  volume  becomes 
5,  the  free  volume  is  now  5—1,  or  4.  The  pressure,  then,  instead  of 
being  doubled,  should  be  as  9  is  to  4,  or  2J  times  as  great.  To  make 
Boyle's  law  cover  such  cases  we  should  state  it  thus:  Pressure  times 
free  volume  equals  K,  where  free  volume  is  total  volume  minus  the 
active  volume  *  of  the  molecules.  If  the  latter  is  designated  by  b  we 
may  then  state  Boyle's  law  as  follows:  P(V—  6)  =K. 

Let  us  next  consider  the  attractive  influence  of  the  molecules. 
This  attraction  tends,  of  course,  to  pull  the  molecules  together  and  thus 
to  decrease  the  volume.  Like  the  volume  correction  discussed  above, 
this  effect  is  noticeable  only  at  high  pressures  when  the  molecules  are 
brought  close  together.  Van  der  Waals,f  who  first  developed  these 
relations,  assumed  with  good  reasons  that  the  intensity  of  this  attrac- 
tion varies  inversely  as  the  square  of  the  total  volume  occupied  by  the 
gas.  If  a  is  taken  as  the  attraction  when  the  volume  is  one  liter,  then 
a/V2  is  the  attraction  for  any  other  volume.  As  we  have  said  above, 
this  attraction  tends  to  decrease  the  volume  of  the  gas.  It,  therefore, 
acts  with  the  external  pressure  and  must  be  added  to  it.  The  total 
pressure  would  be  P-\-a/V2. 

Correcting  Boyle's  law  with  regard  to  both  volume  and  pressure, 
we  should  write  it  : 


This  is  called  "Van  der  Waals'  equation." 

As   previously  mentioned,   deviations    from    Boyle's   law  become 
very  noticeable  in  the  case  of  the  most  perfect  gases  only  at  high  pres- 
sures, for  example,  50  to  100  atmospheres.     At  such  pressures  as  we 
use  in  the  laboratory  (one  or  two  atmospheres)  the  deviations  will  not 
*  "  Active  volume  "  here  probably  means  "  sphere  of  influence." 
f  Kontinuitat  der  gasformigen  und  flussigen  Zustandes  (1899).      [Johannes  D. 
Van  der  Waals,  Professor  of  Physics,  University  of  Amsterdam.]      See  also  Nernst, 
Theoretical  Chemistry,  p.  209 


14  THE  GAS  LAWS 

be  larger  than  the  ordinary  errors  of  observation.  Therefore,  in 
making  use  of  Boyle's  law  for  correcting  gas  volumes  we  assume  that 
the  simple  form,  PF  =  P'F',  holds. 

It  should  be  noted  also  that  the  two  factors  causing  the  deviation 
act  in  opposite  directions,  the  attractive  influence  tending  to  make 
the  volume  smaller  and  consequently  to  decrease  PV,  the  free  volume 
effect  tending  to  prevent  further  compression  and  thus  to  increase 
PV.  Therefore  it  might  be  expected  that  even  a  high  pressure  could 
be  found  where  the  two  would  so  balance  that  the  ordinary  form  of 
Boyle's  law  would  again  hold.  That  this  is  true  may  be  seen  from 
the  following  data  which  refer  to  ethylene  gas :  * 

P  V  PV 

(atmospheres)  (cc.) 

1  1000  1000 

45.8  17.05  781 

84.2  4.74  399 

110.5  4.11  454 

176.0  3.65  643 

282.2  3.33  941 

398.7  3.13  1248 

The  value  of  PV  at  first  grows  smaller  with  increasing  pressure, 
due  to  the  preponderance  of  the  attractive  influence.  At  about  300 
atmospheres  the  two  influences  balance,  and  PV  comes  back  to  its 
original  value.  At  still  higher  pressures  the  free  volume  effect  pre- 
ponderates, making  PV  too  large. 

Those  gases  which  depart  most  widely  from  Boyle's  law  are  the  ones 
which  are  the  most  easily  liquefied.  This  is  due  to  the  fact  that  the 
molecular  attraction  in  these  cases  is  large.  The  following  table  f 
gives  the  values  for  nitrogen.  This  gas,  as  can  be  seen,  departs  much 
less  widely  from  Boyle's  law  than  does  ethylene,  because  it  possesses 
a  smaller  degree  of  intermolecular  attraction.  Nitrogen  is  liquefied 
only  with  extreme  difficulty,  and  so  approaches  closely  the  deportment 
of  a  perfect  gas. 

P  V  PV 

1.00  1.0000  1.0000 

46.50  0.0212  0.9876 

73.00  0.0135  0.9868 

90.98  0.0108  0.9893 

126.90  0.0079  1.0015 

208.64  0.0085  1.0520 

290.93  0.0038  1.1218 

373.30  0.0032  1.2070 

*  Amagat,  Ann.  Chem.,  Phys.,  19,  345. 
t  Amagat,  loc.  tit. 


BOYLE'S  LAW  AND  THE  KINETIC  EQUATION  15 

Boyle's  Law  and  the  Kinetic  Equation. — If  we  assume  that  the 
molecules  of  a  gas  are  perfectly  elastic  and  then  also  agree  that  we  are 
dealing  with  a  dilute  gas  where  the  force  of  attraction  and  the  volume 
occupied  by  the  molecules  are  negligible  factors,  we  can  calculate  Boyle's 
law  quantitatively  in  terms  of  the  mass,  number,  and  velocity  of  the 
molecules :  Consider  a  definite  weight  of  some  gas  contained  in  a  cubical 
vessel  the  sides  of  which  are  of  length  h.  Let  n  be  the  number  of  mole- 
cules, each  of  mass  m,  moving  with  the  average  velocity  s.  The  mole- 
cules will  strike  the  walls  in  every  conceivable  direction,  but  the  velocity 
s  in  each  case  may  be  resolved  into  three  components,  x,  y,  and  z, 
parallel  to  the  edges  of  the  cube,  the  components  being  related  to  the 
original  velocity  as  shown  by  the  equation: 

x2+y2+z2  =  s2 

This  means  simply  that,  although  we  do  not  know  the  direction  in 
which  any  given  molecule  is  moving  and  therefore  cannot  calculate 
the  effect  it  would  have  on  striking  the  wall,  we  do  know  that,  what- 
ever its  direction,  the  effect  it  would  have  on  striking  is  the  same  as  the 
sum  of  the  effects  if  the  collisions  took  place  successively  in  the  direc- 
tions perpendicular  to  the  three  walls  at  right  angles  to  each  other 
with  the  velocities  x,  y,  and  z,  respectively.  We  shall  first  consider 
the  x  component :  Suppose  the  molecule  strikes  the  wall  perpendicularly 
with  the  velocity  x.  Being  perfectly  elastic,  it  rebounds  with  the  same 
velocity,  no  energy  being  lost.  The  momentum  before  the  impact 
was  mx,  and  after  the  impact  it  is  —  mx.  So  the  total  change  of  momen- 
tum due  to  one  impact  is  2mx.  Now  suppose  the  molecule  to  be  moving 
back  and  forth  between  the  two  opposite  walls,  striking  first  one  and 
then  the  other.  If  the  distance  between  the  walls  is  h  the  number  of 
impacts  in  unit  time  will  be  x/h,  and  at  each  impact  the  change  of 
momentum  will  be  2  mx.  The  total  effect,  therefore,  on  the  two  oppo- 
site walls  in  unit  time  will  be  2mx  times  x/h,  or  2mx2/h. 

Now  by  an  identical  process  of  reasoning  we  can  show  that  the 
effects  of  the  other  two  components  on  the  other  four  walls  of  the  cube 
will  be  2my2/h  and  2mz2/h.  The  effect  on  the  six  walls  of  the  cube  due 
to  the  impacts  of  one  molecule  in  unit  time  is  the  sum  of  these  three 
effects,  viz:  2mx2/h-\-2my2/h-\-2mz2/h,  which  may  be  stated,  2m/h 
(x2+y2+?2).  But  since  x2-\-y2-\-z2  =  s2  the  total  effect  becomes  2ms*/h. 
This  is  the  effect  for  one  molecule,  and  since  there  are  n  molecules  in 
the  cube  the  total  effect  for  all  the  molecules  will  be  2mn^/h. 

The  pressure  P  on  unit  surface  is  equal  to  the  total  pressure  divided 
by  the  total  surface,  and  the  latter  is  Qh2.  The  pressure  on  unit  sur- 


16  THE  GAS  LAWS 

face  is  therefore,  2mns2/6h3,  or  mns2/3h3.  But  h3  is  the  volume  of 
the  cube  (V).  Therefore,  the  pressure  P  becomes  mns*/3V  and 
PV  =  mns2/3. 

Boyle's  law  can  be  seen  to  follow  immediately  from  this.  Thus, 
for  a  given  quantity  of  any  gas  the  mass  of  a  single  molecule,  m,  and 
the  number  of  molecules,  n,  are  constants;  and  s  is  a  constant  if  the 
temperature  does  not  change.  Therefore,  the  expression  mm2/ 3  has 
a  constant  value,  for  any  given  temperature,  and  this  makes  P  V  a  con- 
stant, as  it  should  be  according  to  Boyle's  law. 

Perhaps  we  should  again  call  attention  to  the  fact  that  this  regular 
agreement  between  the  observed  and  the  calculated  Boyle's-law 
deportment  is  seen  only  in  the  case  of  a  gas  at  low  pressure. 

The  Law  of  Partial  Pressures. — When  several  gases  are  mixed 
together  each  one  exerts  its  own  pressure  independently  of  the  others, 
and  the  total  pressure  of  the  mixture  is  the  sum  of  the  partial  pressures 
of  the  components.  Thus,  the  air  is  a  mixture  containing  by  volume 
about  78  per  cent  nitrogen,  20  per  cent  oxygen,  1  per  cent  argon,  1  per 
cent  water  vapor,  and  0.03  per  cent  carbon  dioxide,  the  last  two  com- 
ponents being  quite  variable  in  amount.  The  pressure  of  the  whole 
averages,  at  this  altitude,*  about  74  cm.,  and  of  this  total  pressure 
each  gas  present  exerts  its  part  in  proportion  to  its  occurrence.  The 
nitrogen,  therefore,  exerts  a  pressure  of  about  58  cm.;  oxygen  about 
14  cm.;  argon  and  water  vapor  each  somewhat  less  than  1  cm. 

If  from  such  a  mixture  we  remove  one  of  the  components,  the  total 
pressure  will  be  lowered  by  just  the  extent  of  the  partial  pressure  of 
the  component;  and,  knowing  the  total  pressure,  we  can  at  once  cal- 
culate the  percentage  occurrence  of  the  component. 

Temperature  Effects  with  Gases. — When  a  gas  is  heated  its  pres- 
sure increases;  or,  if  the  pressure  is  kept  constant  by  increasing  the 
capacity  of  the  container,  the  volume  increases.  Quantitative  studies 
led  to  the  discovery  that  the  temperature  effect  on  different  gases  was 
very  much  the  same.  Thus,  it  was  found  that  the  volume  of  a  gas 
under  constant  pressure  increased  about  1/273  of  its  volume  at  0°  C. 
for  each  degree  through  which  it  was  heated,  or  that  the  pressure  at 
constant  volume  changed  at  this  rate.  It  should  be  noted  that  this 
is  an  average  rate.  The  rate  of  expansion  for  different  gases  is  not 
quite  the  same,  and  the  rate  for  the  same  gas  depends  somewhat  on  the 
pressure.  The  following  table  gives  the  rate  of  increase  in  pressure 
at  constant  volume  for  several  common  gases :  f 

*  Oberlin,  Ohio,  817  feet  above  sea  level, 
f  Smithsonian  Tables. 


CHARLES'  LAW  AND  THE  ABSOLUTE  TEMPERATURE 


17 


Oxygen  

....1/272.2 

Nitrogen  

....1/272.6 

Nitric  oxide  .  . 

1/272 

Hydrogen.  .  .  . 

....1/273 

Argon 1/272.6 

Helium 1/273 

Carbon  dioxide. .  .  .  1/270.4 
Sulphur  dioxide .  .  .  1/260. 1 
Carbon  monoxide. .  1/272 . 7 

It  will  be  noted  that  here  also,  as  in  the  deviation  from  Boyle's 
law,  the  gases  which  depart  most  widely  from  the  average  rate  are 
those  which  are  most  easily  liquefied,  where  the  attractive  influence 
is  strong.  Note  the  cases  of  nitric  oxide,  carbon  dioxide,  and  sulphur 
dioxide. 

The  deviation  found  in  the  same  gas  at  different  pressures  is  seen 
in  the  following  data  referring  to  air  at  constant  volume :  * 


Pressure 

Coefficient  of 

cm.  of  Hg. 

expansion. 

25.4 

1/273.3 

76 

1/272.8 

200 

1/271 

2000 

1/257 

It  should  be  noted  also  that  the  coefficient  of  expansion  at  constant 
pressure  is  not  always  quite  the  same  as  that  at  constant  volume. 
This  means  that  the  volume  of  a  gas  does  not  always  change  at  quite 
the  same  rate  as  the  pressure.  The  coefficient  of  expansion  of  air  at 
constant  volume  (the  change  in  pressure)  as  given  above  for  ordinary 
conditions,  is  1/272.8.  The  volume  coefficient  for  the  same  conditions 
is  1/272.5.  For  ordinary  calculations  this  difference  may  be  neglected, 
but  it  is  worth  while  to  know  that  it  exists. 

The  statement  that  gases  expand  at  the  average  rate  of  1/273  is 
variously  known  as  Charles' f  Law  and  Gay-Lussac's  t  Law.  The 
value  of  the  constant  is  often  put  in  decimal  form,  when  it  becomes 
0.003663. 

Charles'  Law  and  the  Absolute  Temperature. — Assuming  that  the 
average  coefficient  of  expansion  for  gases  (1/273)  is  correct,  and  assum- 
ing that  the  same  deportment  should  continue,  it  is  evident  that  lowering 
the  temperature  of  a  gas  to  —273°  C.  would  bring  both  its  volume 

*Regnault,  (1842). 

t  Jacques  Alexandre  Cesar  Charles  (1746-1823),  Physicist  at  the  French  Bureau 
of  Standards. 

J  Louis  Joseph  Gay-Lussac  (1778-1850),  French  Chemist  and  Physicist,  noted 
particularly  for  his  law  of  combining  volumes  of  gases. 


18  THE  GAS   LAWS 

and  its  pressure  down  to  zero.  So  far  as  the  pressure  is  concerned 
this  would  probably  happen,  for  at  the  lowest  temperature  which  has 
been  reached  (about  —270°  C.)  practically  all  molecular  motion  seems 
to  have  ceased;  but  the  volume  can  never  become  less  than  the  com- 
bined volume  of  all  the  molecules.*  However  this  may  be,  it  can  i 
be  seen  at  once  that  a  temperature  scale  whose  zero  corresponds  with 
this  hypothetical  zero  of  volume  and  pressure  would  very  much  simplify 
the  calculation  of  gas  volumes.  Such  a  scale  has,  therefore,  been 
devised,  and  is  called  the  "  absolute  scale  "  because  it  is  made  to  cor- 
respond in  an  absolute  way  with  the  changes  of  gas  volume  or  pres- 
sure caused  by  changes  in  temperature.  The  degrees  of  the  absolute 
scale  are  Centigrade  degrees,  but  the  readings  are  always  273°  larger 
than  those  on  the  Centigrade  scale,  simply  because  the  starting  point 
is  273°  lower.  Temperatures  read  on  the  absolute  scale  are  called 
"  absolute  temperatures  "  and  are  designated  by  T. 

Since  the  scale  of  absolute  temperatures  was  constructed  to  cor- 
respond with  the  manner  in  which  gaseous  volumes  and  pressures 
behave  with  respect  to  temperature,  we  can  say  at  once  that  the  changes 
of  volume  and  pressure  are  proportional  to  the  absolute  temperature. 
Mathematically  we  state  these  relations  thus : 

(1)  V  :  V  ::  T  :  T'     at  constant  pressure, 
and 

(2)  P  :  Pf::  T  :  T'     at  constant  volume. 

Combination  of  Boyle's  and  Charles'  Laws. — In  the  last  paragraph 
it  has  been  shown  that  at  constant  pressure  the  volume  of  a  given 
quantity  of  a  gas  varies  with  the  absolute  temperature,  and  at  con- 
stant volume  the  pressure  thus  varies.  It  is  evident  that  in  these 
cases  the  value  of  PF  would  also  be  proportional  to  T.  In  (1),  for 
example,  P  remains  constant  and  from  this 

(3)  PF:  PF'=F:  V'=T:  Tf 
In  (2),  where  F  remains  constant,  we  have 

(4)  PF  :  P'F=P  :  Pf=T  :  T' 

But  these  expressions  include   only  Charles'  law.     If  both  P  and 
F  are  allowed  to  change  simultaneously,  so  as  to  include  Boyle's  law, 

*  This  combined  volume  is  probably  less  at  low  temperatures,  however,  than 
at  high  temperatures,  on  account  of  change  in  the  sphere  of  influence. 


COMBINATION  OF  BOYLE'S  AND  CHARLES'  LAWS  19 

we  make  the  surprising  discovery  that  now  the  value  PF,  and  not 
P  or  V  alone,  changes  with  T.    We  then  have  the  relationship 

(5)  PV  :  P'V'::T  :  T' 

To  prove  that  this  is  true  let  us  suppose  that  the  change  from  the 
original  value  P  V  to  the  new  value  Pf  V  takes  place  in  two  steps  : 

First  let  P  change  to  P'  with  T  constant.  V  will  change  to  a  new 
volume  which  we  may  call  Vx,  but  P'VX  will  still  equal  PV  (Boyle's 
law). 

Now  let  the  temperature  change  to  Tf  while  the  pressure  remains 
constant  at  P'  .  Vx  then  changes  to  V  ',  but,  according  to  (3)  above, 
the  change  in  PF  at  constant  pressure  is  in  the  proportion  T  :  Tr 
(Charles'  law)  which  means  that  P'VX  :  P'F'::  T  :  T'  .  Now,  since 
P'Vx  equals  the  original  PV,  the  whole  change  in  PV  has  been  in 
the  proportion  T  :  T'  . 

Thus,  allowing  Boyle's  law  and  Charles'  law  to  operate  separately, 
we  have  shown  that  the  change  in  PF  is  in  the  proportion  T  :  T'  . 
Evidently  it  makes  no  difference  whether  these  two  laws  operate  sepa- 
rately or  together;  the  final  result  will  be  the  same.  In  any  case  the 
change  in  PF  is  proportional  to  T.  This  is  the  substance  of  equa- 
tion (5). 

In  the  common  problem  of  correcting  gas  volumes  to  standard 
conditions,  equation  (5)  takes  on  the  form  : 

PVT' 

fa\  I7f 


where  P,  F  and  T  are  the  given  conditions  of  pressure,  volume  and 
temperature,  and  F',  P'  and  T'  are  the  volume  sought  for,  the  standard 
pressure  (760  mm.)  and  the  standard  temperature  (273°  abs.).  In 
case  the  conditions  of  temperature  and  pressure  are  not  standard,  P' 
and  T'  may  be  given  any  values  whatsoever,  but  it  should  be  remem- 
bered that  these  represent  the  new  conditions  of  the  problem,  while  P, 
F,  and  T  represent  the  original  conditions. 

Occasionally  we  see  the   combination  of  Boyle's  and  Charles'  laws 
given  in  the  form: 


760(1+0,003670' 

This  really  does  not  differ  in  principle  from  the  common  form; 
for  T'  IT  from  (6)  above  =  273/(273+«),  and  if  we  divide  both  terms 


20  THE  GAS  LAWS 


of  this  fraction  through  by  273  the  numerator  becomes  1  and  the 
denominator  becomes  1+0.00367  t:  the  value  0.00367  is  nothing  more 
than  the  Charles'  law  coefficient,  1/273,  stated  as  a  decimal. 

The  Molecular  Gas-Law  Equation.— If,  as  seen  above,  PV  is  pro- 
portional to  T,  we  may  say  that  PV  equals  a  constant  times  T,  and 
this  we  may  state  as 

PV  =  KT 

If  we  consider  a  mole  of  any  gas  at  273  abs.  and  a  pressure  of  one 
atmosphere,  when  the  volume  is  22.4  liters,  this  equation  becomes 

1X22.4  =  ^273 

If  we  work  out  the  value  of  the  constant  in  liter-atmospheres  we 
find  it  to  be  0.082.  This  constant,  stated  in  various  units,  is  called 
the  "  gas  constant,"  and  is  denoted  by  R.  The  equation  then  becomes 

PV  =  RT 

In  using  this  equation  the  fact  must  not  be  forgotten  that  it  refers  to 
a  mole  *  of  gas.  To  make  the  equation  apply  to  any  other  than  the 
molar  quantity  of  a  gas,  a  factor  (ri)  must  be  introduced  indicating 
the  number  of  moles  present,  f  We  then  write 

PV=nRT 

This  expression  can  be  used  for  the  solution  of  almost  any  gas  problem 
involving  not  only  pressure,  volume,  and  temperature,  but  also  weight. 
It  must  not  be  forgotten,  however,  that  P  stands  for  atmospheres, 
not  millimeters,  V  stands  for  liters,  n  for  moles  or  fraction  of  a  mole, 
and  T  for  the  absolute  temperature.  If  a  problem  arises  in  which  P 
is  the  unknown  we  have 

P  =  nRT/V 

and  if  upon  solution  P  is  found  to  be  0.42,  it  means  that  P  is  0.42  of 
one  atmosphere.  In  millimeters  this  would  be  0.42X760,  or  319.2  mm. 
The  Law  of  Gaseous  Diffusion. — When  a  gas,  such  as  ammonia, 
is  set  free  at  one  end  of  a  long  room,  it  can  after  a  time  be  perceived  at 
the  other.  This  might  be  due  to  convection  currents;  but  if  care  is 

*  A  molecular  weight  in  grams. 

t  If  w  is  the  weight  of  gas  taken  and  M  the  molecular  weight,  n  is,  of  course, 
equal  to  w/M. 


KINETIC  EXPLANATION  21 

taken  to  prevent  these  the  process  is  found  still  to  go  on.  We  believe 
this  to  be  due  to  the  ceaseless  vibratory  motion  of  the  molecules.  Such 
movement  of  one  gas  through  another,  due  to  molecular  motion,  is 
called"  diffusion." 

The  rates  of  diffusion  of  different  gases  are  not  necessarily  the  same. 
It  has  been  found,  for  example,  that  a  heavy  gas  like  oxygen  or  chlorine 
diffuses  much  more  slowly  than  a  light  gas  like  hydrogen  or  helium. 
This  can  be  shown  by  setting  the  gases  free  at  one  end  of  a  long  tube 
placed  horizontally,  and  noting  the  time  required  for  them  to  reach 
the  other  end.  The  matter  of  pressure  and  temperature  must,  of  course, 
be  regulated  and  must  be  the  same  in  each  case.  When  these  precau- 
tions are  taken  it  will  be  found  that  the  heavier  gas  will  always  require 
the  longer  time.  The  same  thing  can  be  shown  also  by  placing  the 
gases,  one  after  the  other,  in  a  container  provided  with  a  minute  opening 
or  porous  diaphragm,  and  causing  them  to  pass  out  under  constant 
pressure.  The  heavy  gas  will  always  require  longer.  A  very  pretty 
method  of  observing  this  difference  is  to  take  two  different  gases  which 
react  visibly  on  each  other,  and  place  them  at  the  opposite  ends  of  a 
tube.  If  the  two  gases  are  of  different  density  the  lighter  one  will  have 
traveled  farther  when  they  come  together. 

Quantitative  studies  have  shown  that  gases  diffuse  at  a  rate  which 
is  inversely  proportional  to  the  square  roots  of  their  respective  densities. 
Thus  hydrogen,  whose  density  is  1/16  as  great  as  that  of  oxygen,  dif- 
fuses four  times  as  fast.  The  densities  of  these  two  gases  are  in  the 
proportion  1  :  16.  The  inverse  ratio  of  the  square  roots  is  Vl6  •  VI, 
or  4  :  1,  which  is  the  ratio  for  the  rates  of  diffusion.  This  is  called 
the  law  of  "  inverse  proportionality."  For  its  discovery  we  are  indebted 
to  Thomas  Graham,*  an  English  chemist.  His  paper  on  this  subject 
appeared  in  the  Philosophical  Magazine  in  1833.  f 

Kinetic  Explanation. — That  the  rates  of  diffusion  of  different  gases 
should  be  as  thus  observed  can  be  seen  when  we  remember  just  what 
factors  enter  into  the  process.  Suppose  we  are  comparing  two  gases 
which  are  either  mixed  together  or  in  contact.  The  temperatures  will 
be  the  same.  If  so,  the  average  kinetic  energy  of  the  molecules  in  the 
two  cases  must  be  the  same;  that  is,  ms2/2  =  mV2/2.  The  densities 
of  the  two  gases  are  proportional  to  the  masses  of  the  single  molecules, 
m  and  m'.  The  rates  at  which  the  gases  will  diffuse  are  proportional 
to  the  molecular  speeds,  s  and  s'.  If  m  is  four  times  m'  then  s2  must 

*  Thomas  Graham  (1805-1869),  Professor  of  Chemistry,  University  of  Lon- 
don. Pioneer  investigator  in  colloid  chemistry  and  gaseous  diffusion.  See  article, 
"  Thomas  Graham."  Essays  on  Historical  Chemistry,  by  Edward  Thorpe. 

f  Phil.  Mag.,  2,  175. 


22  THE  GAS  LAWS 

be  J  of  s'2,  for  by  agreement  the  two  kinetic  energy  expressions  are  to 
be  equal,  s  is  then  \  sf ;  that  is,  where  density  m  is  four  times  as  great 
as  density  mf,  rate  of  diffusion  s  is  \  of  rate  s'.  In  other  words, 
Vm  :  Vm'  ::sf  :  s,  or  the  rates  of  diffusion  are  inversely  proportional 
to  the  square  root  of  the  densities. 

By  reasoning  in  terms  of  the  kinetic  equation  which  we  have  already 
developed,  we  may  calculate  the  absolute  molecular  speeds  for  any 
given  gases,  and  it  will  be  seen  that  these  also  conform  to  the  law  of 
inverse  proportionality.  Let  us  take  the  cases  of  hydrogen  and  oxygen 
gases.  The  kinetic  equation,  as  we  developed  it  under  Boyle's  law, 
was  stated  thus:  PF=rans2/3.  From  this  we  find  that  s=  V^PV/mn. 
If  m  is  the  mass  of  one  molecule  and  n  the  number  of  molecules  in  a 
given  volume,  mn  is  the  weight  of  the  quantity  of  gas  taken.  Suppose 
we  take.  1  liter  of  hydrogen  gas  under  standard  conditions.  Then 
P  =  7Q  cm.  of  mercury;  and  since  the  density  of  mercury  is  13.6,  the 
pressure  of  a  column  of  mercury  76  cm.  high  upon  a  surface  of  1  sq.  cm. 
(unit  surface)  is  76X13.6,  or  1033  gm.  But  since  pressure  is  a  force, 
we  must  express  it  in  dynes.  Therefore  the  pressure,  P,  becomes 
1033X980,  or  1,013,000  dynes.  The  weight  of  1  liter  of  hydrogen, 
mn,  is  0.09  gm.,  and  V  is  1000  cc.  Substituting  these  values  in  the  equa- 
tion above,  we  have 


0.09 

per  second.  If  we  use  oxygen  instead  of  hydrogen  the  data  all  remain 
the  same  except  that  for  mn,  which  becomes  1.429.  In  this  case  the 
calculated  value  for  s  will  be  46,000  cm.  per  second.  We  note,  of  course, 
that  the  calculated  speed  for  hydrogen  is  almost  exactly  four  times 
that  for  oxygen,  a  ratio  almost  exactly  in  accord  with  the  empirical 
ratio. 

Making  use  of  the  fact  that  the  numerator  of  the  fraction  under 
the  radical  above  is  a  constant,  and  that  mn  represents  the  density  (d), 
we  may  simplify  the  expression  to  the  form  s  oo  Vl/d.  The  relative 
speeds  of  any  two  gases  may  then  be  expressed  thus :  s  :  s' ::  Vl/d 
:  Vl/df;  and  from  this  we  obtain  s  :  s' ::  Vd'  :  Vd,  which  is  the  mathe- 
matical statement  of  the  law  of  inverse  proportionality. 

Graham's  Law  and  Molecular  Weights. — Since  molecular  weights 
are  proportional  to  densities  we  may  substitute  molecular  weights 
for  densities  in  the  above  equation,  when  we  have:  s  :  s' ::  Vm/  :  Vm. 
If  we  measure  the  molecular  speed  of  a  gas  as  related  to  one  whose 
speed  and  molecular  weight  are  known,  it  is  evident  that  the  equation 
in  this  form  could  then  be  used  for  the  determination  of  molecular 


EXERCISES  23 

weights.  In  practice  we  measure  the  time  required  for  a  given  volume 
of  a  gas  to  pass  through  a  small  opening  or  a  porous  diaphragm  instead 
of  measuring  the  speed  directly.  The  time  is  evidently  inversely  pro- 
portional to  the  speed,  and  therefore,  directly  proportional  to  the  square 
roots  of  the  molecular  weights.  If,  then,  we  let  t  and  if  denote  the 
respective  times  required  for  the  outflow  of  equal  volumes  of  two  gases, 
one  of  which  is  of  known  molecular  weight,  we  obtain  the  equation: 
t  :  t'::  Vm  :  Vm'.  To  use  this  equation  for  the  determination  of 
molecular  weights  we  need  only  obtain  the  time  of  outflow  for  a  gas 
whose  molecular  weight  is  known  and  then  for  the  gas  under  obser- 
vation, and  substitute  the  values.  If  oxygen  is  used  as  standard  the 
equation  takes  the  form:  t :  £'::  A/32  :  Vm'  where  t  is  the  time  of 
outflow  for  oxygen  and  tf  for  the  given  gas  and  mf  the  unknown  molec- 
ular weight.  For  convenience  the  equation  is  best  put  in  the  form 
w/  =  £/2X32/£2.  Air  may  be  made  the  standard  instead  of  oxygen. 
The  average  molecular  weight  of  air  is  about  29. 

EXERCISES 

1.  Show  just  how  a  gas  exerts  pressure. 

2.  Define  Boyle's  law  in  its  simplest  form. 

3.  Explain  the  expressions:   PV=K,  P=K/V,  V=K/P. 

4.  What  deviations  are  seen  in  the  values  of  PV  at  high  pressures?     Give  two 
reasons  for  these  deviations,  and  show  how  the  two  effects  may  counterbalance. 

6.  Develop  the  equation:   (P+a/F2)(7-6)  =  K. 

6.  Develop  the  kinetic  equation:  PV=mnsz/3,  and  show  from  this  why  Boyle's 
law  must  hold  for  dilute  gases. 

7.  A  flask  holding  215  cc.  contains  air  under  a  pressure  of  742  mm.     Fifty-one 
cc.  of  air  under  a  pressure  of  10  meters  are  forced  in.     What  is  the  final  pressure? 

8.  What  volume  will  be  occupied  at  325  mm.  pressure  by  a  gas  which  occupies 
a  volume  of  450  cc.  at  742  mm.  pressure? 

9.  The  density  of  mercury  at  0°  C.  is  13.54.     When  the  barometer  reads  760  mm. 
and  the  temperature  is  0°  C.,  what  is  the  air  pressure  in  grams  on  1  sq.  cm.  of  sur- 
face?    What  will  be  the  pressure  in  pounds  per  sq.  in.?     (For  conversion  tables 
see  Handbook  of  Chem.  and  Phys.) 

10.  A  barometer  reads  74  cm.     What  would  the  reading  be  if  the  tube  were 
inclined  at  an  angle  of  45°? 

11.  Under  a  pressure  of  one  atmosphere  (760  mm.  of  mercury)  one  liter  of  oxygen 
weighs  1.429  gm.     What  would  one  liter  weigh  under  a  pressure  of  741  mm.? 

12.  A  barometer  stands  at  76  cm.     Three  cc.  of  air  at  this  pressure  are  introduced 
into  the  space  above  the  mercury  in  the  barometer  tube,  when  the  column  sinks 
to  57  cm.     What  volume  does  the  air  now  occupy? 

13.  If  350  cc.  of  dry  air,  measured  at  75  cm.  pressure  and  20°  C.,  is  transferred 
to  a  container  over  water  at  the  same  temperature,  and  the  pressure  is  kept  con- 
stant, what  is  the  final  volume? 

14.  Into  a  250  cc.  vacuous  flask  were  forced  60  cc.  of  nitrogen  under  a  pressure 
of  76  cm.,  200  cc.  of  oxygen  under  a  pressure  of  30  cm.,  and  80  cc.  of  hydrogen  under 


24  THE  GAS  LAWS 

a  pressure  of  42  cm.     What  was  the  partial  pressure  of  each  gas  after  mixing,  and 
what  was  the  total  pressure  of  the  mixture? 

15.  Define  heat  and  temperature  in  terms  of  the  Kinetic  Theory. 

16.  Give  the  quantitative  relations  between  temperature  and  gas  pressure  or 
volume.     What  is  the  average  value  for  the  Charles'  law  coefficient? 

17.  Explain  the  deviations  from  Charles'  law  seen  in  different  gases  or  the  same 
gas  at  different  pressures. 

18.  Show  just  how  the  so-called  "  absolute  "  temperature  scale  has  been  arranged. 
How  related  to  centigrade  temperature? 

19.  Develop  the  equation  PV  :  P'V  ::  T  :  T'. 

20.  Develop  the  general  gas  equation,  PV=nRT,  and  show  the  exact  meaning 
of  each  factor. 

21.  Two  hundred  and  fifty  cc.  of  hydrogen,  measured  at  30°  C.,  are  cooled  to 
—  10°  C.  without  change  of  pressure.     What  is  the  final  volume? 

22.  What  is  the  coefficient  of  expansion  for  sulphur  dioxide  gas?     Two  hundred 
cc.  of  this  gas,  measured  at  10°  C.,  were  heated  to  125°  C.     What  was  the  amount 
of  expansion? 

23.  One  thousand  cc.  of  air,  measured  at  15°  C.,  and  755  mm.  pressure,  was 
increased  to  1200  cc.  by  warming.     The  final  pressure  was  740  mm.     What  was  the 
final  temperature? 

24.  What  decrease  in  temperature  will  be  necessary  to  reduce  300  cc.  of  air  at 
20°  and  750  mm.  pressure  to  a  volume  of  200  cc.  at  730  mm.  pressure? 

25.  Under  standard  conditions  a  liter  of  hydrogen  weighs  0.0896  gm.     What 
will  a  liter  weigh  if  collected  at  25°  C.  and  742  mm.  pressure? 

26.  A  quantity  of  nitrogen  measuring  400  cc.  at  30°  C.  and  752  mm.  pressure 
was  compressed  to  a  volume  of  100  cc.  at  0°  C.     What  pressure  was  applied? 

27.  When  2.7  liters  of  air  saturated  with  water  vapor  at  18°  C.  were  drawn 
through  a  calcium  chloride  tube    the  water  was  removed  and  was  found  to  weigh 
0.0412  gm.      What  was    the  pressure    of    the   water  vapor?     (Use  the  equation 
PV  =  nRT  in  the  calculation.) 

28.  Under  what  pressure  will  10  gm.  of  nitrogen  gas  occupy  32  liters  at  20°  C.? 
(Use  same  methods  as  in  27.) 

29.  If  air  were  allowed  to  diffuse  through  a  porous  partition  would  the  diffused 
air  have  the  usual  composition?     In  what  way  would  it  differ? 

30.  If  a  certain  volume  of  nitrogen  diffuses  through  a  porous  cylinder  in  10.27 
min.  how  much  time  will  be  required  for  the  diffusion  of  an  equal  volume  of  carbon 
dioxide,  conditions  being  the  same? 

31.  If  a  mixture  of  ether  vapor  and  ammonia  were  set  free  at  the  end  of  a  room, 
would  both  constituents  of  the  mixture  be  perceived  at  the  other  end  at  the  same 
time?     Explain  in  detail. 

32.  Starting  with  the  kinetic  equation,  develop  the  proportion  t  :  t' ::  \/d  :  ^fd'. 

33.  Show  by  substitution  in  the  kinetic  equation  that  the  average  speed  of  the 
hydrogen  molecule  is  four  times  that  of  the  oxygen  molecule. 

34.  Develop  the  equation  m'  =  t'2m/t2. 

35.  Show  that  when  two  gases  are  in  equilibrium  with  respect  to  the  kinetic 
energy  of  the  molecules  the  molecular  speeds  must  be  inversely  proportional  to  the 
square  roots  of  their  respective  densities. 

36.  When  is  the  average  kinetic  energy  of  the  molecules  of  one  gas  equal  to  that 
of  another? 


CHAPTER  III 
LAWS  GOVERNING  CHANGE  OF  STATE 

IN  Chapter  I  we  studied  the  general  characteristics  of  gases,  liquids, 
and  solids.  In  this  chapter  we  shall  study  the  facts  concerning  the 
changes  from  one  state  to  another  and  the  laws  governing  these  changes. 
The  detailed  study  of  equilibrium  relations  between  phases  we  shall 
leave  for  a  later  chapter. 

A  Saturated  Vapor. — If  a  volatile  liquid  is  placed  in  an  open  dish, 
so  that  the  molecules  as  they  leave  the  surface  are  free  to  diffuse  away, 
the  liquid  sooner  or  later  goes  completely  over  into  the  gaseous  state. 
If,  however,  the  containing  vessel  is  so  arranged  that  the  escaping 
molecules  are  confined  within  certain  limits,  as,  for  example,  in  the 
upper  part  of  a  stoppered  bottle  partially  filled  with  liquid,  then  the 
case  is  quite  different.  The  molecules  moving  about  in  the  free  space 
above  the  liquid  are  bound  in  a  certain  average  percentage  of  their 
excursions  to  strike  the  surface  and  be  held  there.  As  their  number 
increases,  the  rate  of  their  return  to  the  liquid  will  also  increase,  until 
finally  they  will  be  returning  as  fast  as  they  come  off.  The  liquid  and 
its  vapor  are  then  in  equilibrium;  or,  to  use  the  common  expression, 
the  vapor  is  said  to  be  "  saturated." 

Vapor  Pressure  a  Function  of  Temperature. — Other  conditions 
remaining  the  same,  the  density  and  pressure  of  a  saturated  vapor 
remain  perfectly  constant.  If  we  should  attempt  to  increase  the  density 
by  compression  we  should  only  cause  the  molecules  to  return  to  the 
liquid  a  little  more  rapidly,  when  the  former  state  of  equilibrium  would 
immediately  be  restored.  But  there  is  just  one  thing  that  can  change 
the  pressure  of  a  saturated  vapor,  and  that  is  a  change  in  temperature. 
A  rise  in  temperature  and  a  consequent  increase  in  the  average  kinetic 
energy  of  the  molecules  is  attended  by  a  more  rapid  escape  from  the 
surface  and  so  by  a  higher  pressure  of  the  vapor  phase.  This  means 
that  the  pressure  of  a  vapor  when  in  equilibrium  with  the  liquid  is  an 
exact  function  of  the  temperature.  This  is  well  shown  by  the  following 
table  which  gives  the  pressure  of  aqueous  vapor  in  equilibrium  with 
liquid  water  at  various  temperatures: 

25 


26  LAWS  GOVERNING  CHANGE  OF  STATE 

VAPOR  PRESSURE  OF  WATER  IN  MILLIMETERS 


Temperature 

Pressure 

Temperature 

Pressure 

Temperature 

Pressure 

0 

4.6 

11 

9.8 

21 

18.5 

1 

4.9 

12 

10.5 

22 

19.7 

2 

5.3 

13 

11.2 

23 

23.9 

3 

5.6 

14 

11.9 

24 

22.2 

4 

6.0 

15 

12.7 

25 

23.6 

5 

6.5 

16 

13.5 

26 

25.1 

6 

7.0 

17 

14.4 

27 

26.5 

7 

7.4 

18 

15.4 

28 

28.1 

8 

8.0 

19 

16.3 

29 

29.8 

9 

8.6 

20 

17.4 

30 

31.8 

10 

9.2 

100 

760.0 

Use  of  Values  of  Water  Vapor  Pressure. — Our  most  frequent  use 
of  the  values  for  aqueous  vapor  pressure  is  in  the  measurement  of  gases 
over  water  where  we  must  think  of  the  space  occupied  by  the  gas  as 
being  also  occupied  by  water  vapor  at  its  saturation  pressure.  This 
gives  us  another  application  of  the  law  of  partial  pressures;  and  since 
we  have  already  discussed  that  law  we. need  not  take  up  the  matter 
here,  except  to  say  that  in  this  special  case  we  can  always  know  the 
partial  pressure  of  the  water  vapor  if  we  know  the  temperature.  We 
shall  have  many  opportunities  for  application  of  this  principle  in  the 
succeeding  sections. 

Vapor  Pressure  and  Boiling  Point. — When  the  vapor  pressure  of 
a  liquid  equals  the  pressure  of  the  atmosphere  above  it,  bubbles  of  vapor 
forming  inside  the  liquid  are  able  to  expand  and  come  to  the  surface. 
Bubbles  will  then  continue  to  form  throughout  the  liquid,  and  we  say 
the  liquid  is  "  boiling."  Evidently  the  temperature  at  which  this 
phenomenon  will  occur  depends,  first  on  the  liquid,  and  second,  on  the 
external  pressure.  Thus  water  would  boil  at  25°  C.  if  the  pressure 
of  the  atmosphere  were  23.6  mm.  What  we  understand,  however,  as 
the  true  boiling  point  of  a  liquid  is  the  temperature  at  which  its  vapor 
pressure  equals  the  standard  atmosphere  (760  mm.).  According  to 
this,  the  true  boiling  point  of  water  is  100°  C.  The  vapor  pressure  of 
liquid  oxygen  reaches  one  atmosphere  at  —182.5°  C.,  that  of  liquid 
carbon  dioxide  at  —79°  C.,  that  of  ether  at  34.5°  C.  and  that  of  mercury 
at  357°  C.  These  are,  therefore,  the  boiling  points  of  the  liquids 
named. 

Superheating  and  Means  of  Preventing. — As  we  have  seen  above, 
a  liquid  is  bound  to  boil  when  the  vapor  which  is  formed  possesses  the 


SUPERHEATING  AND  MEANS  OF  PREVENTING  27 

same  pressure  as  the  atmosphere.  It  is  possible,  however,  under  certain 
conditions  to  have  the  temperature  at  the  proper  point,  or  even  above, 
without  having  the  vapor  form  at  all.  Thus,  if  water  in  a  tall  beaker 
is  heated  at  the  bottom  the  temperature  may  be  brought  above  100°  C. 
and  the  water  still  not  boil.  The  water  is  then  said  to  be  "  super- 
heated." The  condition  is  naturally  a  rather  unstable  one;  and  if  in 
some  way  a  single  bubble  of  steam  can  be  started  near  the  bottom, 
most  violent  boiling  will  immediately  ensue.  This  violent  action  follow- 
ing superheating  is  accompanied  by  a  sharp  clicking  sound  and  is  usually 
spoken  of  as  "  bumping."  It  is  sometimes  vigorous  enough  to  endanger 
a  glass  container. 

The  phenomenon  of  superheating  is  caused  by  the  lack  of  any  free 
space  at  the  point  where  the  heat  is  applied  into  which  the  liquid 
may  vaporize.  Ordinarily,  however,  the  steam  bubbles  form  spon- 
taneously at  various  points  on  the  sides  or  bottom  of  the  container 
without  allowing  a  high  degree  of  superheating.  This  is  especially 
true  if  the  liquid  contains  air  or  some  other  gas  which  may  form  bubble 
nuclei.  When  the  air  is  all  boiled  out,  bumping  is  more  likely  to  occur. 
Thus,  water  which  has  been  exposed  to  the  air  and  has  become  satu- 
rated with  it  boils  gently  and  continuously  at  first,  because  the  air 
bubbles  brought  out  by  the  heat  form  the  starting  points  for  the  steam 
bubbles.  Later,  when  the  air  is  boiled  out  this  same  water  boils  inter- 
mittently and  with  considerable  tendency  to  bump.  A  slight  greasiness 
on  the  inside  of  the  container  lessens  the  tendency  for  some  liquids, 
notably  water,  to  bump,  and  any  substance  which  dissolves  off  this 
film  will  tend  to  cause  bumping.  Thus  a  solution  of  alcohol  or  sodium 
hydroxide  in  water  is  almost  sure  to  bump  because  of  this  solvent 
action. 

Superheating'  may  be  prevented  in  several  ways.  The  first  is  to 
place  in  the  liquid  some  porous  substance  which  entraps  air  and  thus 
offers  open  spaces  into  which  the  liquid  may  vaporize.  A  piece  of 
unglazed  porcelain  or  pumice  serves  the  purpose  very  well.  Another 
method  is  to  place  in  the  liquid  some  substance  which  will  slowly  gener- 
ate gas  bubbles.  Zinc,  for  example,  may  be  put  into  a  solution  of 
sodium  hydroxide,  the  hydrogen  generated  bringing  about  the  desired 
result.  A  third  method  is  to  have  a  long  tube  extending  down  to  the 
bottom  of  the  container  and  to  slowly  bubble  air  through  this.  But 
perhaps  the  neatest  method  is  to  place  in  the  liquid  a  long  slender  tube 
having  the  bore  sealed  at  a  point  about  one  centimeter  from  the  bottom. 
The  little  inverted  cup  thus  formed  carries  air  (free  space)  down  to  the 
point  where  the  heat  is  being  applied,  and  so  effectually  prevents 
superheating.  When  one  of  these  "  boiling-tubes  "  is  present  in  a 


28  LAWS  GOVERNING   CHANGE  OF  STATE 

liquid  practical!}'  all  the  steam  bubbles  have  their  origin  in  the  cup, 
and  are  seen  issuing  from  the  end  of  the  tube  in  a  continuous  stream. 

Humidity  and  Dew  Point. — The  atmosphere  always  contains  some 
water  vapor,  the  amount  present  depending  on  weather  conditions. 
Its  pressure  is  usually  considerably  lower  than  the  saturation  value. 
Thus,  as  seen  from  the  table,  page  26,  the  saturation  pressure  at  20°  C. 
is  17.4  mm.  On  a  very  wet  day  at  20°  the  pressure  of  the  water  vapor 
in  the  air  may  reach  95  per  cent  of  this  value.  In  a  very  dry  atmos- 
phere the  water  vapor  pressure  may  be  as  low  as  20  per  cent  of  the 
saturation  value,  or  even  lower.  These  percentages  representing  the 
degrees  of  saturation  are  spoken  of  as  the  "  humidity  "  of  the  atmos- 
phere. Suppose,  for  example,  that  on  a  certain  day  when  the  temper- 
rture  is  25°  C.  the  pressure  of  water  vapor  in  the  air  is  8  mm.  The 
^turation  value  for  this  temperature,  as  seen  from  the  table,  is  23.5  mm. 
j.  he  humidity,  therefore,  is  8/23.5,  or  33.9  per  cent. 

What  we  call  "  dew  point  "  is  the  temperature  to  which  an  unsatu- 
rated  atmosphere  must  be  lowered  that  it  may  become  saturated. 
This  can  best  be  explained  by  use  of  an  example:  Suppose  the  temper- 
ature on  a  certain  day  is  24°  C.  and  the  humidity  80  per  cent.  The 
saturation  pressure  at  24°  is  22.2  mm.  The  pressure  of  the  water 
vapor  in  the  air  is  80  per  cent  of  this,  or  17.76  mm.  By  interpolation 
from  the  table  we  find  that  at  20.33°  this  would  be  the  saturation  value. 
Therefore,  if  an  atmosphere  80  per  cent  saturated  at  24°  C.  were  cooled 
to  20.33°  C.  it  would  be  found  saturated  at  this  lower  temperature. 
The  "  dew  point  "  for  this  particular  case  is,  therefore,  20.33°  C.  The 
term  "  dew  point  "  is  used  in  this  connection  because  at  the  dew-point 
temperature  in  a  given  case  a  slight  film  of  moisture  (dew)  begins  to 
be  deposited  on  the  surface  of  objects.  This  is  often  seen  when  a  glass 
of  cold  water  is  allowed  to  stand  in  a  rather  moist  atmosphere.  The 
temperature  in  the  immediate  neighborhood  of  the  glass  is  brought 
bebw  the  dew  point,  and  tiny  droplets  of  water  are  seen  condensing 
on  the  surface. 

It  is  scarcely  necessary  to  mention  that  the  experimental  determi- 
nation of  dew  point  lends  itself  at  once  to  the  accurate  calculation  of 
humidity.  This,  in  fact,  is  a  common  method  of  determining  humidity. 
A  volatile  liquid,  like  ether,  is  placed  in  a  thin  glass  bottle,  together 
with  a  thermometer.  Rapid  evaporation  of  the  liquid  is  induced  by 
bubbling  through  it  a  current  of  air.  The  temperature  is  thus  reduced, 
and  when  the  dew  point  is  reached  a  film  of  moisture  is  seen  condensing 
on  the  outer  surface  of  the  glass.  The  temperature  then  indicated  on 
the  thermometer  is  the  dew  point.  By  consulting  the  table  the  satu- 
ration value  for  the  dew-point  temperature  is  then  found  and  compared 


MELTING  AND  MELTING  POINT  29 

with  the  saturation  value  for  the  room  temperature.  The  per  cent 
humidity  is  thus  calculated  at  once.  For  example;  by  blowing  air 
through  ether  a  temperature  of  6.4°  C.  was  reached,  when  a  film  of 
moisture  was  seen  on  the  glass.  Interpolating  from  the  table,  we 
found  that  the  saturation  pressure  for  6.4°  was  7.16  mm.  The  room 
temperature  was  24°  C.  At  this  temperature  the  saturation  value 
is  22.2  mm.  The  humidity  of  the  air  was,  therefore,  7.16/22.2,  or 
32.2  per  cent. 

Melting  and  Melting  Point. — Melting  is  the  process  of  changing 
from  the  solid  to  the  liquid  form.  Melting  point  is  the  temperature 
at  which  melting,  or  fusion,  occurs.  Crystalline  solids  alone  show 
definite  melting  points.  Such  amorphous  substances  as  glass  or  pitch, 
having  no  orderly  structure,  act  like  viscid  liquids,  and  only  become 
less  and  less  viscid  as  heat  is  applied. 

As  we  have  noted  in  Chapter  I,  crystalline  solids  are  characterized 
by  a  definite  lattice-work  structure.  This  structure  is  brought  about 
by  intermolecular  and  interatomic  forces  and  is  broken  down  only 
when  the  kinetic  energy  of  the  molecules  is  able  to  overcome  these 
forces.  Moreover,  since  the  intermolecular  forces  for  any  given  solid 
are  of  perfectly  definite  intensity,  and  since  kinetic  energy  is  proportional 
to  temperature,  we  should  expect  that  the  breaking  down  of  the  crystal- 
line structure  of  any  solid  would  require  a  perfectly  definite  temper- 
ature. That  it  does  is  a  matter  of  experience,  for  we  know  that  no 
property  of  a  true  solid  is  more  definite  and  characteristic  than  its 
melting  point.  Ice  melts  at  such  a  definite  temperature  that  we  cali- 
brate our  thermometers  by  immersing  them  in  a  mixture  of  melting 
ice  and  water;  and  one  of  the  main  criteria  of  purity  and  identity 
among  organic  compounds  is  the  melting  point. 

Melting  Point  and  Pressure. — The  melting  (or  freezing)  temper- 
ature is  nearly,  but  not  quite,  independent  of  the  pressure.  If 
melting  is  accompanied  by  increase  in  volume,  an  increase  in  pressure 
will  retard  the  process,  and  a  higher  temperature  will  be  required. 
If  melting  is  accompanied  by  decrease  in  volume,  increase  in  pressure 
will  aid  the  process  and  the  substance  will  melt  at  a  lower  temperature, 
as  in  the  case  of  ice.  An  increase  of  one  atmosphere  in  pressure  lowers 
the  melting  point  of  ice  by  0.0074°  C.  This  explains  the  fact  that  one 
can  pack  snow  readily  when  it  is  near  the  freezing  point,  but  not  when 
the  temperature  is  too  low.  If  the  temperature  is  at,  say,  0.0074°  C. 
an  extra  pressure  of  one  atmosphere  applied  with  the  hands  will  cause 
the  ice  to  begin  melting,  and  when  the  pressure  is  removed  the  water 
thus  formed  again  freezes,  cementing  the  crystals  together.  If  the 
temperature  were  at  —2°  or  —3°  it  is  evident  that  no  one  would  be 


30  LAWS   GOVERNING   CHANGE  OF  STATE 

able  to  apply  the  tremendous  pressure  required  to  start  the  melting. 
The  reason  that  the  melting  point  of  ice  is  ordinarily  so  very  definite 
is  that  the  pressure  of  the  atmosphere  remains  very  constant,  and  that 
relatively  large  changes  are  necessary  to  cause  an  appreciable  difference. 

Sublimation. — It  is  a  matter  of  common  experience  to  find  solids 
which  show  an  appreciable  vapor  pressure,  by  which  we  understand 
that  certain  solids  may  go  over  into  the  vapor  form  without  melting. 
That  ice  thus  shows  a  distinct  vapor  pressure  is  shown  by  the  fact  that 
clothes  dry  when  hung  on  a  line  in  freezing  weather.  We  have  all 
noticed  also  how  moth-balls  (naphthalene)  decrease  in  size  or  even 
vanish  altogether  after  being  allowed  to  remain  in  a  trunk  of  clothes 
for  a  long  time.  Indeed  the  efficacy  of  the  compound  as  a  moth-killer 
is  due  to  the  vapor  which  is  constantly  given  off.  Any  substance 
which  thus  passes  into  the  vapor  state  without  melting  is  said  to  "  sub- 
lime "  (from  the  Latin,  meaning  "  to  rise  on  high  ")• 

The  process  of  sublimation  is  used  quite  largely  as  a  means  of  puri- 
fying substances.  For  example,  a  sample  of  impure  iodine  may  be 
placed  between  watch  glasses  and  gently  heated,  when  the  pure  product 
rises  as  a  vapor  and  crystallizes  on  the  upper  glass.  The  impurities 
are  usually  left  behind,  not  having  an  appreciable  vapor  pressure. 

The  Cooling  Effect  of  Evaporation. — When  a  volatile  liquid  like 
ether  is  allowed  to  evaporate  on  the  hand,  a  feeling  of  cold  is  experi- 
enced. When  ether  is  allowed  to  stand  in  an  open  dish  for  a  time,  a 
thermometer  inserted  in  the  liquid  will  indicate  a  temperature  several 
degrees  below  that  of  the  room.  The  same  effect  is  seen  with  any 
volatile  liquid.  Even  water,  which  is  only  slightly  volatile  at  room 
temperature,  will,  if  left  standing  in  an  open  dish,  be  found  to  be  slightly 
lower  in  temperature  than  water  in  a  closed  bottle  standing  by  its  side.* 

The  Kinetic  Theory  explains  these  facts  as  follows:  The  temper- 
ature of  a  liquid  is  proportional  to  the  average  kinetic  energy  of  its 
molecules.  But  these  molecules  are  not  all  moving  at  the  same  rate. 
Some  are  moving  slowly,  others  more  rapidly.  The  molecules  at  the 
surface  are  in  general  held  down  by  the  attraction  of  their  associates, 
but  those  which  possess  more  than  the  average  speed  and  kinetic  energy 
gradually  break  away  from  the  others  and  fly  off  into  the  space  above. 
This  process  tends  to  leave  behind  a  larger  and  larger  proportion  of  the 
more  slowly  moving  molecules,  a  fact  which  alone  would  be  recorded 
as  a  lowering  of  the  temperature.  Besides  this,  the  molecules  in  sepa- 
rating or  spacing  out  are  compelled  to  work  against  their  own  inter- 
attraction,  and  will  thus  experience  a  slowing  down  in  speed.  This 

*  The  degree  of  lowering  will  depend  on  the  humidity  of  the  air,  dry  air  promoting 
rapid  evaporation,  and  consequent  greater  lowering  of  the  temperature. 


THE  QUANTITATIVE  HEAT  RELATIONS  31 

will  again  be  recorded  as  a  lowering  of  the  temperature.  This  effect 
is  particularly  pronounced  at  very  low  pressures  where  the  spacing- 
out  process  is  unimpeded  and  is  very  complete.  Hence  the  pronounced 
cooling  (even  freezing)  of  a  liquid  evaporating  under  the  effect  of  an 
air  pump. 

In  many  cases  these  two  factors  are  the  only  causes  operating  to 
lower  the  temperature  of  an  evaporating  liquid.  In  some  cases,  how- 
ever, another  factor  enters  in,  viz.,  the  breakdown  of  small  aggregates 
of  molecules.  Take  the  case  of  water:  According  to  recent  investi- 
gations,* liquid  water  is  made  up  quite  largely  of  the  aggregates  (H2O)2 
and  (H2O)3,  as  well  as  H^O,  the  three  forms  having  been  named  di- 
hydrol,  tri-hydrol,  and  mono-hydrol,  respectively.  When  water  passes 
into  vapor  the  aggregates  must  first  be  broken  down  into  the  simple 
molecules,  and  this  process  requires  the  consumption  of  much  kinetic 
energy  or  heat.  In  the  case  of  such  liquids  as  water,  therefore,  the 
cooling  effect  of  evaporation  is  caused  by  three  factors,  namely,  the 
passing  away  of  the  more  rapidly  moving  molecules,  the  spacing-out 
process,  and  the  breaking  down  of  molecular  aggregates. 

The  Quantitative  Heat  Relations. — As  would  be  expected,  the 
quantitative  relations  for  the  heat  of  evaporation  are  perfectly  definite. 
Take  again  the  case  of  water:  The  proportion  of  the  three  phases, 
mono-,  di-,  and  tri-hydrol,  depends  on  the  temperature,  low  temperatures 
favoring  the  presence  of  tri-hydrol  and  high  temperatures  of  mono- 
hydrol;  but  for  any  temperature  the  relative  amounts  of  the  three 
phases  are  fixed  and  definite.  Since  in  the  process  of  evaporation  it 
is  only  the  mono-hydrol  which  passes  off,  the  evaporation  of  one  gram 
or  one  mole  would  certainly  involve  the  breaking  down  of  a  perfectly 
definite  number  of  the  aggregates,  and  would  thus  require  the  expendi- 
ture of  a  perfectly  definite  amount  of  heat  energy.  Moreover,  since 
according  to  Avogadro's  law  the  final  spacing  of  the  molecules  will, 
for  a  given  temperature  and  pressure,  be  the  same,  it  should  require 
the  same  expenditure  of  energy  to  bring  about  the  spacing.  Finally, 
by  the  simple  law  of  averages,  the  moving  away  of  the  more  rapid 
molecules  should  always  produce  the  same  cooling  effect  if  the  condi- 
tions of  temperature  and  pressure  are  the  same.  From  this  reasoning 
it  follows  that  the  total  amount  of  heat  energy  expended  in  vaporizing 
one  gram  of  water  at,  say,  100°  C.  and  one  atmosphere  pressure  should 
always  be  the  same.  This  we  find  to  be  a  fact.  The  vaporization  of 
one  gram  of  water,  at  100°  C.  and  one  atmosphere  pressure,  requires 
the  expenditure  of  538.7  calories  of  heat  energy.  This  value  is  called 
the  "  heat  of  vaporization  "  of  water. 

*  Transactions  of  the  Faraday  Society,  6,  71  (1910). 


32 


LAWS  GOVERNING  CHANGE  OF  STATE 


Effect  of  Temperature  and  Pressure. — The  heat  of  vaporization 
is  somewhat  affected  by  changes  in  temperature  and  pressure.  In 
general,  the  heat  of  vaporization  will  be  greater  for  lower  temperatures 
in  the  cases  of  all  associated  liquids  like  water,  because  at  lower  tem- 
peratures the  aggregates  are  larger  or  more  numerous.  It  will  be  greater 
also  at  lower  pressures  because  the  molecules  have  to  be  spaced  out 
farther.  The  data  in  the  following  table,*  referring  to  the  heat  of 
vaporization  of  water,  will  show  these  relations: 


Pressure 
(in  mm.) 

Temperature 

Heat  of 
Vaporization 

760 

100° 

538.7 

289 

75 

554.0 

92.3 

50 

568.4 

23.7 

25 

582.3 

4.6 

0 

595.4 

Heat  of  Condensation  Equals  Heat  of  Evaporation. — It  scarcely 
needs  to  be  said  that  the  heat  given  off  by  a  vapor  in  condensing  is 
exactly  equal  to  the  heat  required  for  its  vaporization.  The  only 
difference  is  that  the  changes  take  place  in  reverse  order  and  produce 
the  opposite  effect.  Thus  the  molecules,  in  returning  from  their  spaced- 
out  condition,  are  speeded  up  by  their  attraction  for  each  other,  the 
more  rapidly  moving  molecules  return  to  the  liquid,  and  the  aggregates 
are  re-formed,  all  these  changes  producing  heat.  The  common  method 
of  determining  heat  of  vaporization  makes  use  of  this  fact  by  finding 
how  much  heat  is  given  off  in  the  condensation  of  a  known  weight  of 
vapor  at  some  definite  temperature  and  pressure. 

Heat  of  Fusion. — The  only  substances  which  have  a  definite  heat 
of  fusion  are  the  crystalline  solids.  The  atoms  in  such  substances 
are  held  in  perfectly  definite  relative  positions  and  are  free  to  vibrate 
only  within  small  fixed  limits.  When  the  kinetic  energy  of  these  atoms 
is  raised  to  the  point  where  they  are  able  to  tear  themselves  away  from 
this  restraint  the  substance  is  at  its  melting  point.  Suppose  a  few 
atoms  have  been  thus  separated  to  form  a  liquid.  Any  further  addition 
of  heat  would  tend  to  speed  up  the  vibrations  of  these  molecules;  but 
if  this  happened  their  kinetic  energy  would  at  once  be  imparted  to  the 
atoms  of  the  melting  solid,  causing  more  atoms  to  melt  away.  From 
this  it  can  be  seen  that  just  so  long  as  the  melting  solid  is  kept  in  con- 

*  For  more  complete  data  see  "  Handbook  of  Chem.  and  Phys."  (The  Chemical 
Rubber  Co.)  topic,  "  Heat  of  vaporization  of  saturated  steam." 


CONDENSATION  OF  A  SATURATED  VAPOR  33 

tact  with  the  resulting  liquid,  the  heat  applied  does  not  raise  the  temper- 
ature, but  is  used  up  in  furthering  the  change  of  state. 

In  this  case,  just  as  in  the  case  of  vaporization,  the  amount  of  heat 
required  is  definite  and  characteristic  for  any  solid.  Thus,  one  gram 
of  ice  at  0°  C.  requires  80  calories  of  heat  to  melt  it,  leaving  the  resulting 
water  still  at  0°.  The  fact  that  large  amounts  of  heat  are  consumed 
in  melting  ice  carries  with  it  some  important  consequences.  The 
spring  season,  for  example,  is  retarded  in  the  neighborhood  of  great 
lakes,  thus  preventing  the  premature  development  of  fruit  buds,  which 
would  later  be  killed  by  frosts.  The  melting  of  ice,  too,  makes  it  pos- 
sible to  ship  perishable  foods  long  distances  by  keeping  the  temperature 
below  the  point  where  bacteria  can  propagate  rapidly.  The  following 
table  gives  the  heat  of  fusion  of  several  common  solids: 


Substance 

Heat  of  Fusion 

Aluminum  

76.8 

Ammonia    

108.0 

Copper 

42  0 

Ice  
Mercury 

80.0 
2  82 

Sodium  nitrate  
Sulphur                            .  . 

64.87 
9.37 

Zinc  

28.13 

Condensation  of  a  Saturated  Vapor. — We  have  already  shown  that 
saturation  is  a  case  of  equilibrium,  in  which  the  gaseous  molecules  are 
coming  from  the  liquid  and  returning  to  it  at  the  same  rate.  A  satu- 
rated vapor  can  be  condensed  either  by  lessening  the  amount  of  space  or 
by  lowering  the  temperature.  Lessening  the  amount  of  free  space 
increases  momentarily  the  concentration  of  the  vapor  and  consequently 
the  rate  at  which  the  molecules  return  to  the  liquid ;  but  this  process 
immediately  restores  the  state  of  equilibrium,  with  the  result  that  the 
pressure  is  the  same  as  before.  If  we  lower  the  temperature  of  the 
liquid  we  decrease  the  rate  at  which  the  molecules  come  off;  and  if  the 
rate  of  their  return  remains  the  same  it  is  plain  that  the  vapor  mole- 
cules at  once  become  depleted;  in  other  words,  the  vapor  is  condensed. 

Condensation  of  an  Unsaturated  Vapor  or  Gas.— The  case  of  an 
unsaturated  vapor  is  somewhat  more  complicated.  Suppose  we  have 
a  bottle  which  is  completely  vacuous,  and  allow  a  single  drop  of  some 
volatile  liquid,  such  as  water,  to  enter.  We  shall  probably  see  thir, 
small  amount  pass  entirely  into  vapor;  and  we  may  probably  repeat 


34  LAWS  GOVERNING  CHANGE  OF  STATE 

the  process  several  times  without  bringing  the  pressure  of  the  vapor  up 
to  the  saturation  point.  This  vapor  acts  now  like  any  other  gas,  obey- 
ing Boyle's  law,  Charles'  law,  etc.  If  it  is  compressed,  its  pressure 
will  increase ;  if  it  is  expanded,  its  pressure  will  decrease.  If,  however, 
the  process  of  compression  is  carried  far  enough,  its  pressure  will 
finally  be  brought  to  the  saturation  point.  The  liquid  then  appears, 
and  after  that  we  have  again  the  simple  case  of  equilibrium  described 
above. 

But  we  have  seen  that  the  pressure  of  a  vapor  at  saturation  depends 
upon  the  temperature.  If  the  temperature  is  raised  we  shall  have  to 
compress  our  vapor  until  it  has  a  higher  pressure  before  it  will  pass 
over  into  the  liquid  form.  To  make  this  clear,  suppose  the  temperature 
is  18°  C.  At  this  temperature,  water  vapor  at  saturation  has  a  pressure 
of  15  mm.  Now  suppose  a  drop  of  water,  upon  evaporating  inside 
the  vacuous  bottle,  gives  a  pressure  of  10  mm.  We  must  then  com- 
press the  vapor  until  it  occupies  two-thirds  of  its  present  volume  before 
saturation  will  be  reached  and  condensation  begin.  Again,  suppose 
the  temperature  is  34°  C.  The  vapor  pressure  of  water  at  this  temper- 
ature is  40  mm.  Suppose  the  pressure  of  the  vapor  in  the  bottle  is 
still  10  mm.;  we  must  now  compress  this  vapor  until  it  occupies  one- 
fourth  of  its  present  volume  before  condensation  will  begin.  Thus, 
with  rising  temperature  it  appears  that  greater  and  greater  pressure 
is  required  to  start  condensation.  This  we  understand  to  be  due  to 
the  fact  that  rise  of  temperature  implies  greater  kinetic  energy  on  the 
part  of  the  molecules  and  therefore  a  greater  tendency  to  remain  in  the 
gaseous  condition. 

Critical  Temperature  and  Pressure. — If  we  raise  the  temperature 
of  a  liquid  sufficiently,  we  finally  reach  a  point  where  the  kinetic  energy 
of,  the  molecules  becomes  so  great  that  their  attractive  influence 
can  no  longer  overcome  it,  no  matter  how  great  the  pressure. 
When  this  temperature  is  reached  it  makes  no  difference  how  much 
we  compress  a  gas,  we  cannot  cause  it  to  liquefy.  The  only  available 
method  then  is  to  lower  the  temperature,  thus  decreasing  the  kinetic 
energy  of  the  molecules  and  giving  the  cohesive  forces  a  chance  to  act. 
This  temperature,  at  which  pressure  alone  will  not  liquefy  a  gas,  is  called 
the  "  critical  temperature  "  of  the  gas.  The  vapor  pressure  of  a  gas 
at  its  critical  temperature  is  called  its  "  critical  pressure."  At  this 
critical  point  the  condition  of  a  gas  is  a  peculiar  one.  The  line  of  sepa- 
ration between  gas  and  liquid  becomes  indistinct  and  fades  away,  and 
gas  and  liquid  are  identical. 

The  critical  temperature  of  carbon  dioxide  is  31.8°  C.,  when  the 
vapor  pressure  is  75  atmospheres.  If  a  glass  tube  half  filled  with  the 


MODERN  METHOD  OF  LIQUEFYING  GASES 


35 


liquid  and  sealed  off  be  gently  warmed  until  the  temperature  is  31.8°, 
we  see  the  meniscus  separating  the  liquid  and  gas  slowly  flatten  and 
fade  away.  At  this  temperature  the  contents  of  the  tube  are  homoge- 
neous and  perfectly  invisible.  If  the  temperature  of  this  invisible  gas 
is  allowed  to  fall  slowly  a  slight  mist  appears  when  the  critical  point 
is  reached,  and  the  next  instant  the  contents  of  the  tube  are  seen  to  sepa- 
rate into  two  layers,  liquid  and  gas. 

The  following  table  shows  the  critical  temperatures  and  pressures 
for  several  gases.     The  pressures  are  given  in  atmospheres : 


t°C. 

P 

t°C. 

P 

Water            

364 

195 

Ethylene 

10 

52 

Alcohol 

243 

63 

Methane 

-  95 

55 

Ether  

197 

36 

Oxygen  

—  118 

51 

Chlorine 

144 

84 

Nitrogen 

-146 

35 

Ammonia  

130 

115 

Hydrogen.  

-225 

20 

Carbon  Dioxide      .    . 

31.8 

73 

Helium 

-268 

2  3 

Modern  Method  of  Liquefying  Gases. — In  the  earlier  work  on  lique- 
faction of  gases  the  matter  of  critical  temperature  and  pressure  was  not 
understood.  The  gases  mentioned  in  the  table  above,  as  far  down  as 
ethylene,  were  liquefied  by  pressure  alone.  This  was  because  their  criti- 
cal temperatures  lay  at  or  above  ordinary  laboratory  temperatures.  But 
oxygen,  nitrogen,  and  several  other  gases  were  subjected  to  enormous 
pressures  without  liquefying.  Modern  research  has  shown  this  failure 
to  be  due  to  the  fact  that  the  critical  temperatures  of  these  gases  lie  far 
below  the  range  of  laboratory  temperatures,  and  has  directed  atten- 
tion to  the  necessary  condition,  namely,  the  attainment  of  low  temper- 
atures. 

For  the  purpose  of  getting  these  low  temperatures  two  methods 
are  available.  The  first  method  makes  use  of  the  cooling  effect  of 
evaporation.  We  have  already  seen  that  evaporation  consumes  great 
quantities  of  heat  energy,  and  have  also  noted  that  the  effect  becomes 
very  pronounced  if  the  vapor  formed  is  rapidly  removed  by  means  of 
a  pump,  that  is,  if  the  pressure  is  reduced.  Thus,  liquid  ethylene  may 
be  made  to  boil  at  —130°  C.  if  the  pressure  is  sufficiently  reduced. 
Since  this  is  below  the  critical  temperature  of  oxygen  it  is  possible,  by 
using  boiling  liquid  ethylene  as  a  cooling  bath,  to  liquefy  oxygen,  pro- 
vided a  pressure  of  something  less  than  50  atmospheres  (the  critical 
pressure)  is  applied  at  the  same  time. 


36 


LAWS  GOVERNING  CHANGE   OF  STATE 


The  second  method  of  obtaining  low  temperatures  is  based  on  what 
is  called  the  Joule-Thomson  *  effect.  This  effect  may  be  briefly 
explained  as  follows:  When  a  gas  is  allowed  to  expand  from  a  high  to 
a  low  pressure  there  is  usually  a  decided  lowering  of  the  temperature. 
This  is  due  mainly  to  the  intermolecular  attraction,  one  of  the  causes 
which  lead  to  the  deviations  from  Boyle's  law.  As  the  molecules  fly 
apart  their  motion  is  retarded  by  this  attraction,  their  average  kinetic 
energy  is  lowered,  and  the  temperature  falls.  Due  to  the  tremendous 


FIG.  2. — Liquid  Air  Apparatus. 


kinetic  energy  of  their  molecules  and  the  vanishingly  small  intermolec- 
ular attraction,  the  cases  of  hydrogen  and  helium  at  ordinary  temper- 
atures are  anomalous;  but  if  through  previous  cooling  their  kinetic 
energy  is  reduced,  these  gases  then  come  into  line  with  the  others,  and 
show  the  same  effect  upon  expansion. 

The  modern  liquid-air  apparatus,  such  as  the  Linde,  makes  use 
of  the  Joule-Thomson  principle.  The  gas,  under  a  pressure  of  about 
200  atmospheres,  is  allowed  to  expand  through  a  small  opening  down 

*  Sir  William  Thomson  (Lord  Kelvin)  (1824-1907)  Professor  of  Natural  Phi- 
losophy at  Glasgow.  Noted  physicist.  Laid  the  first  Atlantic  cable. 


EXERCISES  37 

to  a  pressure  of  about  1  atmosphere.  In  this  way  the  temperature 
is  greatly  lowered.  The  gas  thus  cooled  is  led  back  over  the  tube 
containing  the  compressed  gas,  thus  cooling  it.  The  cooler  compressed 
gas  upon  expanding  through  the  opening,  drops  to  a  still  lower  temper- 
ature than  did  the  first  portion.  Thus  the  effect  becomes  cumulative, 
and  the  temperature  of  the  expanding  gas  drops  lower  and  lower  until 
liquefaction  ensues.  Hydrogen  and  helium,  due  to  their  anomalous 
behavior,  must  first  be  cooled  by  means  of  a  bath  of  liquid  air  before 
being  allowed  to  expand. 

The  above  sketch  shows  the  essential  parts  of  the  apparatus.  A  is 
a  compressing  pump.  B  is  a  cooling  coil  intended  to  remove  the  heat 
due  to  compression  or  to  pre-cool  such  gases  as  hydrogen.  C  is  the 
valve  through  which  the  expansion  occurs.  Note  that  the  -tube  con- 
taining the  highly  compressed  gas  runs  inside  the  larger  tube.  The 
expanded  and  cooled  gas  passes  back  through  the  annular  space  between 
these  two  tubes,  the  outer  tube  thus  acting  as  a  cooling  jacket. 


EXERCISES 

1.  Describe  the  condition  of  saturation  as  applied  to  a  vapor  or  gas. 

2.  How  are  vapor  pressure  and  boiling  point  related?      At  what  temperature 
would  water  boil  if  the  pressure  were  reduced  to  21  mm? 

3.  Why  do  liquids  sometimes  li  bump  "  when  boiled?     Describe  four  methods 
of  preventing  this. 

4.  Suppose  the  humidity  of  the  air  is  57.3  per  cent  and  the  temperature  is  26°  C. 
What  would  be  the  dew  point? 

5.  The  temperature  on  a  certain  day  was  25°  C.     The  dew  point  was  found  to 
be  10.2°  C.     What  was  the  humidity? 

6.  What  change  in  volume  would  occur  if  the  water  vapor  were  removed  from 
4.5  liters  of  air  saturated  at  22°  C.,  assuming  that  the  pressure  remains  constant 
at  74  cm.? 

7.  A  student  wishes  to  dry  out  a  flask.     To  do  this  he  conducts  into  it  a  very 
rapid  stream  of  cold  air,  leaving  the  flask  cold  in  the  meantime.     Correct  this  pro- 
cedure in  the  light  of  your  study  of  vapor  pressure. 

8.  Show  why  the  melting  of  a  crystalline  solid  should  occur  at  a  definite  temper- 
ature. 

9.  How  is  melting  point  related  to  pressure?     Example? 

10.  Discuss  the  topic  "  sublimation." 

11.  Show  why,  in  any  case,  the  evaporation  of  a  liquid  lowers  the  temperature. 

12.  Show  why  the  heat  of  vaporization  is  abnormally  high  in  the  case  of  water 
and  a  few  other  liquids. 

13.  Show  why  the  quantity  of  heat  required  to  evaporate  a  definite  weight  of 
a  liquid  is  definite  and  characteristic. 

14.  How  is  the  heat  of  evaporation  affected  by  changes  in    temperature    and 
pressure? 

16.  Define  "  heat  of  evaporation  "  and  give  the  standard  value  for  water. 


38  LAWS  GOVERNING  CHANGE  OF  STATE 

16.  Find  the  topic  "  Heat  Equivalent  of  Vaporization,"  Handbook  of  Chem. 
and  Phys.,  and  suggest  an  explanation  for  the  great  differences  seen  between  the 
heats  of  vaporization  of  different  liquids. 

17.  How   is   liquid   ammonia   used  for  refrigerating  purposes?     Would   liquid 
SO2  do  as  well?    Why? 

18.  Define  "  heat  of  fusion  ";   what  is  meant  by  saying  that  the  heat  of  fusion 
of  ice  is  80  calories? 

19.  One  hundred  gm.  of  water  at  a  certain  temperature  was  mixed  with  100  gm. 
of  ice.     When  the  ice  had  melted  the  temperature  of  the  water  was  0°  C.     What 
was  the  original  temperature  of  the  water? 

20.  What  would  be  the   relative  effectiveness  of    ice  at  0°  and  water  at  0°  as 
refrigerating  agents? 

21.  Can  ice  be  warmed  above  0°  C.?    Why?     Can  it  be  cooled  below  0°  C.? 

22.  Show  just  how  the  process  of  fusion  consumes  heat  and  prevents  rise  of  temper- 
ature. 

23.  How  does  a  saturated  vapor   differ  from  an   unsaturated  vapor?     How  do 
both  act  when  compressed?     When  cooled? 

24.  What  is  meant  by  critical  temperature  and  pressure? 

25.  How  may  a  gas  be  liquefied  by  taking  advantage  of  the  cooling  effect  of 
evaporation  ? 

26.  Explain  the  Joule-Thomson   effect  and  its  bearing  on   the  liquefaction  of 
gases. 

27.  What  gases  may  be  liquefied  by  pressure  alone  at  ordinary  temperature? 
Why  not  all? 

28.  Explain  the  working  of  the  Linde  liquid-air  machine.     State  and  explain 
the  special  treatment  necessary  in  the  cases  of  hydrogen  and  helium. 

29.  The  mole  of  ether  is  74  gm.,   and  the  vapor  pressure  at  20°  C.  is  433  mm. 
What  weight  of  ether  is  required  to  saturate  50  cc.  at  this  temperature?     (Use  the 
molecular  equation  PV  =  nRT.} 


CHAPTER  IV 
AVOGADRO'S  LAW  AND  MOLECULAR  WEIGHTS 

Development  of  Avogadro's  Law.  —  Avogadro's  law  (sometimes 
called  Avogadro's  hypothesis)  grew  out  of  a  study  of  the  law  of  com- 
bining volumes  of  gases  and  the  laws  of  definite  and  multiple  propor- 
tions. It  was  known  that  the  elementary  gases  combined  in  very 
simple  proportions  by  volume,  for  example,  1:1,  1:2,3:1,  etc.; 
never  in  such  fractional  ratios  as  1  :  1.32.  It  was  also  known  that  the 
weight  relations  in  these  same  cases  were  very  definite.  Moreover, 
the  laws  of  Boyle  and  Charles  applied  in  almost  exactly  the  same  way 
to  all  gases,  any  small  exceptions  being  easily  accounted  for.  From  a 
careful  study  of  such  facts  as  these,  Avogadro  came  to  the  very  logical 
conclusion  that  under  the  same  conditions  of  temperature  and  pressure 
equal  volumes  of  all  gases  contain  the  same  number  of  molecules. 

We  have  already  noted,  in  Chapter  I,  that  the  study  of  Brownian 
movement  enables  us  to  measure  the  number  of  molecules  in  a  liter 
or  cubic  centimeter  of  any  gas,  assuming  that  the  law  of  equipartition 
of  energy  holds  for  molecules  as  well  as  for  visible  particles.  We  have 
also  mentioned  the  surprising  fact  that  the  number  in  the  same  volume 
is  always  the  same  if  the  conditions  of  temperature  and  pressure  are  the 
same.  We  may  also  reason  out  the  same  thing  in  a  slightly  different 
way:  Brownian  movement  has  proved  the  validity  of  the  law  of  equi- 
partition of  energy,  which  means  that  all  the  particles  in  a  system, 
no  matter  how  much  they  vary  in  size,  have  the  same  average  kinetic 
energy.  Temperature  is  a  measure  of  kinetic  energy.  Therefore,  if 
two  different  gases  are  at  the  same  temperature,  the  average  kinetic 
energy  of  their  molecules  must  be  the  same.  The  pressure  of  a  gas 
is  proportional  to  the  average  kinetic  energy  of  the  molecules  and  to 
the  number  of  molecules  in  a  unit  volume.*  If,  then,  two  different 
gases  are  at  the  same  temperature  and  the  same  pressure,  both  the 
kinetic  energy  of  the  molecules  and  the  number  of  molecules  in  unit 
volume  must  be  the  same.  This,  again,  is  Avogadro's  law. 

Practically  the  same  reasoning  may  also  be  put  into  mathematical 

*PF  =  wns2/3,  which  may  be  written  as  -  ——Xn.     But  since  equal  volumes 

3    2 

are  being  compared  V  drops  out,  and  P  is  seen  to  be  proportional  to  msz/2  and  to  n. 

39 


40  AVOGADRO'S  LAW  AND   MOLECULAR  WEIGHTS 

form  as  follows:  The  kinetic  energy  of  a  single  molecule  =  ras2/2  for  one 
gas,  and  raY2/2  for  another.  The  temperature  of  the  two  gases  is  the 
same.  Therefore,  the  average  kinetic  energy  of  the  molecules  is 
the  same,  or 

(1)  ms2/2  =  wY2/2 

If  the  pressures  and  volumes  of  the  two  gases  are  the  same,  then 
PV  =  P'V.  We  know  that  P  V  is  a  constant  for  any  gas  if  the  temper- 
ature is  constant,  and  have  shown  that  this  is  equal  to  mn^/3.  P'V, 
therefore,  equals  mVs/2/3,  and  if  PV  =  P'Vf\  then 


(2) 

If  we  now  divide  equation  (2)  by  equation  (1)  we  have  2/3n  =  2/3n'. 
Therefore,  n  =  nf,  which  we  were  to  prove. 

Deviation  from  Avogadro's  Law.  —  It  must  not  be  forgotten  that 
such  calculations  as  the  above  are  based  on  the  assumption  that  we 
are  working  with  perfect  gases,  which  is  never  the  case.  We  have 
seen  that  gases  do  not  perfectly  obey  the  ordinary  gas  laws,  and  it  is 
certainly  not  to  be  expected  that  they  should  perfectly  obey  Avogadro's 
law.  The  correspondence  is  the  same  as  in  the  other  cases.  If  the 
gases  are  at  low  pressure  and  are  far  from  the  point  of  liquefaction 
Avogadro's  law  will  hold  almost  perfectly.  If  the  gas  is  under  high 
pressure  or  is  near  its  point  of  liquefaction  Avogadro's  law  holds  only 
approximately. 

Molecular  Weights.  —  If  equal  volumes  of  different  gases  at  the  same 
temperature  and  pressure  contain  the  same  number  of  molecules,  then 
the  weights  of  such  equal  volumes  must  stand  in  the  same  relation 
as  the  weights  of  the  individual  molecules.  Thus,  if  any  given  volume 
of  oxygen  gas  weighs,  under  the  same  conditions  of  temperature  and 
pressure,  16  times  as  much  as  an  equal  volume  of  hydrogen  gas,  a  single 
molecule  of  oxygen  must  be  16  times  as  heavy  as  a  single  molecule  of 
hydrogen.  We  are  thus  able,  by  use  of  Avogadro's  principle,  to  deter- 
mine the  relative  weights  of  the  molecules  of  all  gases  and  of  all  sub-' 
stances  which  can  be  gotten  into  the  gaseous  condition. 

But  it  would  hardly  be  a  convenient  system  which  simply  told  us 
that  the  molecules  of  one  gas  were  so  many  times  heavier  than  those 
of  another.  A  much  more  convenient  system  would  be  one  in  which 
an  arbitrary  value  had  been  assigned  to  the  molecular  weight  of  some 
one  substance,  and  in  which  those  of  other  substances  were  given  values 
showing  the  proper  weight  relation  to  this  and  to  each  other.  This  has 
been  done.  The  molecular  weight  of  oxygen  has  been  made  32,  and 
the  molecular  weights  of  other  substances  are  given  values  which  are 


THE  ABSOLUTE  WEIGHTS  OF  MOLECULES  41 

related  to  this  value,  just  as  their  weights  as  gases  are  related  to  the 
weight  of  oxygen  gas.  Thus,  chlorine  gas  is  2.2162  times  as  heavy  as 
oxygen  when  under  the  same  conditions.  Therefore  we  make  its  molec- 
ular weight  2.2162  times  32,  or  70.92. 

Just  why  the  value  32  was  chosen  for  the  molecular  weight  of  oxygen 
we  can  explain  more  fully  after  we  have  taken  up  the  Atomic  Theory; 
but  the  following  explanation  may  be  given  in  advance.  According 
to  the  atomic  hypotheses,  molecules  are  made  up  of  atoms,  which  also, 
of  course,  have  certain  relative  weights.  When  the  relative  weights 
of  the  different  atoms  were  determined  it  was  found  that  that  of  hydro- 
gen was  the  smallest.  It  was,  therefore,  given  the  value  1.  Now, 
there  is  very  good  evidence  that  the  molecule  of  hydrogen  contains 
2  atoms.  Hence,  its  molecular  weight,  using  the  same  unit  of  measure- 
ment, should  be  2.  Finally,  oxygen  gas  is  15.95  times  as  heavy  as 
hydrogen;  its  molecular  weight  should  therefore  be  15.95  times  2,  or 
31.9.  Lately  it  has  been  found  more  convenient  to  do  away  with 
the  fractional  value  for  oxygen  and  make  it  exactly  32.  This,  of  course, 
leaves  the  value  for  hydrogen  fractional  (2.016),  but  this  is  not  con- 
sidered so  important,  since  hydrogen  is  a  much  less  convenient  stand- 
ard for  molecular  weight  determination. 

The  Absolute  Weights  of  Molecules. — It  will  be  noted,  of  course, 
that  the  values  for  the  molecular  weights  obtained  by  the  above  method 
are  merely  relative.  This  means  that  when  we  say  the  molecular 
weight  of  oxygen  is  32  we  do  not  mean  that  it  is  32  gm.  or  32  lb.,  but 
simply  32  as  related  to  an  arbitrary  unit  equal  to  about  half  the  mole- 
cular weight  of  hydrogen.  Knowing,  as  we  do,  the  number  of  mole- 
cules in  a  liter  of  gas  under  standard  conditions,  we  are  able  to  calcu- 
late the  absolute  weight  of  a  single  molecule  of  any  gaseous  substance. 
Take  an  example  or  two:  The  weight  of  a  liter  of  oxygen  gas  under 
standard  conditions  is  1.429  gm.  The  number  of  molecules  in  one 
liter  of  any  gas  under  standard  conditions  we  have  already  shown  to 
be  2.7X1022  (see  page  4).  Dividing,  we  find  the  weight  of  a  single 
molecule  of  oxygen  to  be  5.29  X 10 ~23  gm.  The  weight  of  one  liter  of 
hydrogen  gas  under  standard  conditions  is  0.0899  gm.  The  number 
of  molecules  will  be  the  same  as  in  the  case  of  oxygen.  Dividing,  there- 
fore, we  obtain  for  the  weight  of  a  single  molecule  of  hydrogen  the 
value  0.332  XKT23  gm. 

Proceeding  in  the  same  way,  it  would  be  possible  to  determine  the 
absolute  weight  of  a  molecule  of  any  element  or  compound  which  could 
be  obtained  in  the  gaseous  condition.  But  the  question  naturally 
arises:  What  special  value  would  these  absolute  weights  have?  They 
would  be  very  complicated.  They  would  be  related  in  exactly  the  same 


42 


AVOGADRO'S  LAW  AND   MOLECULAR   WEIGHTS 


way  as  the  relative  weights.  Thus  the  absolute  value  for  oxygen 
given  above,  is  15.95  times  that  of  hydrogen.  Nothing  could  be  done 
with  them  that  cannot  be  done  with  the  relative  weights.  They  have 
no  advantage  at  all,  and  they  may  sometimes  be  found  to  have  some 
disadvantage;  for  the  value  given  above  for  the  number  of  molecules 
in  one  liter  of  a  gas  may  have  to  be  revised,  and  such  revision  would 
force  us  to  change  the  value  of  every  molecular  weight.  It  is  quite 
evident,  therefore,  why  we  use  the  relative,  rather  than  the  absolute, 
values. 

Gram-molecular  or  Molar  Weights. — For  convenience  in  making 
up  solutions  and  planning  quantitative  reactions,  it  is  often  necessary 
to  have  molecular  weights  stated  in  grams.  For  a  molecular  weight 
thus  stated,  we  use  variously  the  terms  "  gram-molecular  weight," 
"  molar  weight,"  or  simply  "  mole."  Thus,  a  mole  of  oxygen  is  32  gm., 
a  mole  of  hydrogen  is  2  gm.,  a  mole  of  chlorine  is  70.92  gm.  It  will 
be  noted  that  the  relative  values  are  in  no  wise  changed;  the  only 
difference  is  that,  whereas  the  simple  molecular  weights  are  stated  in 
abstract  numbers,  moles  are  stated  in  the  concrete  values  we  have 
to  work  with  in  the  laboratory. 

Molar  Volume. — Since  molecular  weights  are  the  relative  weights 
of  equal  volumes  of  different  gases,  a  mole  of  any  gas  under  standard 
conditions  should  occupy  the  same  volume.  Just  what  this  volume 
is  may  be  calculated  by  dividing  the  molar  weight  of  any  gas  by  the 
weight  of  one  liter  under  standard  conditions.  Thus  a  mole  of  hydrogen 
weighs  2.016  gm.  and  one  liter  of  hydrogen  under  standard  conditions 
weighs  0.0899  gm.  The  volume  occupied  by  one  mole  is,  therefore, 
2.016/0.0899,  or  22.42  liters.  This  is  the  molar  volume  for  hydrogen. 
The  molar  volume  for  other  gases  should  be  the  same;  but,  due  to  the 
fact  that  gases  are  not  quite  perfect  in  their  behavior,  the  molar  volume 
varies  slightly.  Hydrogen  is  nearly  a  perfect  gas,  and  for.  this  reason 
its  molar  volume  may  be  considered  as  standard.  The  following  table 
gives  the  weight  of  one  liter  and  the  molar  volume  of  several  gases: 


Weight  of  1  Liter 

Molar  Volume 

Hydrogen  
Oxygen  ....                        .    . 

0.0899 
1  .  4291 

22.42 
22.39 

Nitrogen 

1  2507 

22.40 

Carbon  monoxide 

1  2500 

22.40 

Ammonia  
Carbon  dioxide  
Hydrogen  chloride  .  .    .         

0.7621 
1.9766 
1.6410 

22.35 
22.26 
22.22 

Chlorine                                            .    . 

3  2200 

22.02 

Sulphur  dioxide  

2.9296 

21.88 

DETERMINATION  OF  MOLECULAR  WEIGHTS  43 

The  correspondence  here  is,  of  course,  the  same  as  that  in  the  case 
of  Avogadro's  law,  since  the  underlying  principle  is  the  same.  The 
so-called  permanent  gases  come  very  close  to  the  ideal  behavior  and 
have  a  molar  volume  of  about  22.4,  while  those  gases  which  are  easily 
liquefied  depart  quite  appreciably  from  the  ideal,  and,  therefore,  have  a 
somewhat  different  molar  volume.  For  ordinary  calculations  we  assume 
the  molar  volume  to  be  22.4,  which  is  somewhere  near  an  average  value. 

It  is  interesting  to  note  that  the  deviation  in  the  case  of  the  easily 
liquefied  gases  is  in  such  a  direction  as  to  make  the  molar  volume  some- 
what smaller.  This  is  undoubtedly  due  to  the  fact  that  in  these  cases 
the  intermolecular  attraction  is  large.  This  tends  to  bring  the  mole- 
cules closer  together  and  so  increase  the  number  of  molecules  per  liter 
above  what  it  should  be  according  to  Avogadro's  law.  With  more 
molecules  per  liter  the  number  of  liters  required  for  the  mole  is  less. 

Determination  of  Molecular  Weights. — Since  the  molar  volume 
represents  approximately  a  mole  of  any  gas,  its  use  constitutes  a  very 
simple  and  convenient  method  for  the  determination  of  molecular 
weights.  All  that  is  necessary  is  to  obtain  the  substance  as  a  gas  and 
then  find  what  weight  of  it  is  required  to  occupy  22.4  liters  when  calcu- 
lated to  standard  conditions.  The  result  will  be  the  molar  weight. 
The  fact  that  some  substances  are  not  gaseous  at  0°  and  760  mm.  pres- 
sure does  not  hinder  the  use  of  the  method.  It  is  only  necessary  that 
it  be  possible  to  convert  the  substance  into  a  gas  at  some  workable 
temperature.  A  known  volume  can  be  collected  at  this  temperature, 
and  then  calculated  down  to  standard  conditions  by  use  of  the  gas 
laws.  The  fact  that  the  gas  will  liquefy,  or  even  solidify,  before  stand- 
ard conditions  are  reached  makes  no  difference  with  the  calculation; 
at  those  temperatures  where  the  substance  is  gaseous  it  will  obey 
Avogadro's  law  and  the  other  gas  laws,  as  well  as  any  gas  which  is 
not  very  far  removed  from  the  point  of  liquefaction  would  be  expected 
to  do.  Thus,  water  is  either  a  liquid  or  a  solid  at  0°  C.,  but  at  temper- 
atures above  100°  it  is  a  gas,  and  in  this  condition  the  spacing  of  the 
molecules  is  practically  the  same  as  for  any  other  gas.  We  may  there- 
fore determine  the  weight  of  a  known  volume  of  this  gaseous  water 
at  some  known  temperature  and  pressure,  and  then  calculate  what 
this  volume  would  become  if  it  were  a  gas  at  0°  and  760  mm.  pressure. 
We  can  then  calculate  the  weight  of  22.4  liters  under  these  conditions, 
and  this  will  represent  approximately  the  molecular  weight. 

The  method  outlined  above  for  determination  of  molecular  weights 
is  essentially  the  same  as  the  original  method  outlined  by  Dumas,* 

*  Jean  B.  A.  Dumas  (1800-1884),  great  French  teacher  and  investigator.    Thorpe's 

"  Essays,"  p.  318. 


44 


AVOGADRO'S  LAW  AND   MOLECULAR  WEIGHTS 


the  French  chemist,  in  1826.  We  may  note  that  this  method  has  lately 
been  more  or  less  superseded  by  one  invented  by  the  German,  Victor 
Meyer,*  involving  the  same  principle  but  using  different  apparatus. 

According  to  Meyer's  method,  a 
known  weight  of  substance  is 
vaporized  in  a  jacketed  tube  filled 
with  air.  The  volume  of  gas 
formed  is  found  by  measuring  the 
volume  of  air  displaced.  The 
accompanying  sketch  shows  the 
essential  arrangement  of  the 
apparatus.  Water,  or  some  other 
liquid,  is  boiled  in  the  jacket  A, 
and  when  the  temperature  becomes 
constant  the  cork  B  is  removed 
and  a  capsule  containing  the 
weighed  sample  is  dropped  in. 
The  cork  is,  of  course,  instantly 
replaced  before  vaporization  oc- 
curs. The  displaced  air  is  col- 
lected and  measured  in  the  tube 
C. 

It  is  worth  noting  that  the 
calculation  of  a  molecular  weight 
from  the  weight  of  a  known  volume 
of  a  gas  may  be  very  much 
shortened  by  use  of  our  funda- 
mental gas  equation,  PV  =  nRT. 
As  we  have  before  explained,  n 
represents  the  number  of  moles  of 
gas,  and  its  value  is  obtained  by 
dividing  the  weight  of  gas  (w)  by 
We  may,  therefore,  write  the  equation  as 


FIG.  3. — Victor  Meyer's  Molecular 
Weight  Apparatus. 


its  molar  weight  (M). 


From  this  we  obtain 


PV  =  wRT/M 
M  =  wRT/PV 


Take  the  following  example: 

Three  hundred  cc.  of  gaseous  ether  at  74  cm.  pressure  and  at  100°  C. 
weight  0.706  gm.     What  is  the  molecular  weight? 


Victor  Meyer  (1848-1897)  Professor  of  Chemistry,  University  of  Heidelberg. 


EXERCISES  45 

From  this  we  obtain:    w  =  0.706,    r=373,  P=74/76,   and  F=0.3. 
Substituting,  we  have: 

0.706X0.082X373X76 
74X0.3 

Solving,  we  find  M  to  be  74. 

EXERCISES 

1.  Upon  what  facts  did  Avogadro  found  his  law? 

2.  Show  how,  from  consideration  of  kinetic  energy,  temperature,  and  pressure, 
Avogadro's  law  must  follow. 

3.  Prove  Avogadro's  law  by  use  of  the  kinetic  equation. 

4.  How  closely  does    Avogadro's  law  apply  in    ordinary  cases?     Explain.     In 
what  cases  is  there  the  greatest  deviation? 

5.  Define  "  molecular  weight,"    (a)  without  the  use  of  molar  volume,    (6)  in 
terms  of  molar  volume.     How  is  molar  volume  determined? 

6.  What  deviations  are  seen  in  the  case  of  molar  volume?     Explain. 

7.  The  weight  of  22.4  liters  of  air,  under  standard  conditions,  is  28.95  gm.     If 
air  were  a  single  gas  this  would  be  its  molecular  weight.     We  may  call  it  the  "  aver- 
age molecular  weight  of  the  mixture."     Find  the  weight  of  one  liter  under  standard 
conditions. 

8.  The  molecular  weight  of  nitrogen  is  28,  of  chlorine  71,  of  hydrogen  2,  of  hydro- 
gen chloride  36.5,  and  of  ammonia  17.     Find  the  weight  of  one  liter  of  each  under 
standard  conditions.     (The  weights  thus  obtained  are  usually  called  "  densities." 
Note  that  they  stand  in  the  same  relation  as  the  molar  weights.     The  only  difference 
is  that  densities  are  the  weights  of  single  liters,  and  molar  weights  are  the  weights 
of  22.4  liters.) 

9.  What  is  the  average  molecular  weight  of  a  mixture  containing  80  per  cent 
nitrogen,  18  per  cent  oxygen,  and  2  per  cent  water  vapor,  by  volume? 

10.  The  molecular  weight  of  a  substance  is  46.     What  is  the  weight  of  one  liter 
of  it  in  the  gaseous  form,  at  20°  C.  and  742  mm.  pressure? 

11.  What  is  the  molar  volume  at  20°  C.  and  740  mm.  pressure?     (Use  the  molec- 
ular gas  equation.) 

12.  A  10-liter  flask  contains  nitrogen  under  a  pressure  of  22  mm.  and  at  a  temper- 
ature of  21°  C.     What  weight  of  nitrogen  is  present?     (Use  the  molecular  gas  equa- 
tion.) 

13.  Several  cubic  centimeters  of  liquid  ether  were  placed  in  a  bulb  holding  289  cc. 
The  bulb  was  then  immersed  in  water  at  a  temperature  of  88°  C.  until  the  ether  had 
boiled  away,  displacing  the  air  and  leaving  the  bulb  filled  with  gaseous  ether.     When 
the  weight  of  the  vacuous  bulb  was  subtracted  the  ether  vapor  was  found  to  weigh 
0.707  gm.     The  barometer  reading  was  738  mm.     Calculate  the  molecular  weight 
of  ether  from  these  data. 

14.  Describe  the  Victor  Meyer  method  for  determining  molecular  weights. 

15.  Using  the  data  of  Problem  13  calculate  the  molecular  weight  of  ether,  by 
means  of  the  equation  PV  =  wRT/M. 


CHAPTER  V 
THE  QUANTITATIVE  LAWS  OF  CHEMICAL  COMBINATION 

The  Law  of  Constant  Composition. — From  the  earliest  times  it  has 
probably  been  recognized  that  to  prepare  a  given  compound  it  was 
necessary  to  put  together  the  same  ingredients  and  to  use  them  in  about 
the  same  proportion.  Not  until  someone  denied  it,  however,  was  the 
law  of  constant  composition  really  proved.  In  1799  Berthollet,*  a 
French  chemist,  made  the  statement  that  the  properties  and  compo- 
sition of  compounds  were  dependent  on  the  amount  of  the  ingredients 
taken  for  their  preparation.  Proust,  f  a  countryman  of  his,  immedi- 
ately set  about  disproving  this  statement.  He  analyzed  a  large  number 
of  minerals  coming  from  all  parts  of  the  world,  and  in  many  cases  also 
prepared  the  same  compounds  artificially.  The  controversy  }  between 
Proust  and  Berthollet  lasted  eight  years,  but  in  the  end  Proust  was 
completely  victorious.  His  conclusions  we  give  in  his  own  words: 
"  We  are  forced  to  recognize  that  the  composition  of  true  compounds 
is  as  invariable  as  their  properties:  between  pole  and  pole  they  are 
identical  in  these  two  respects.  The  cinnabar  of  Japan  has  the  same 
properties  and  composition  as  that  of  Spain :  silver  chloride  is  identically 
the  same,  whether  obtained  from  Peru  or  Siberia:  in  all  the  world  there 
is  but  one  chloride  of  sodium,  one  saltpeter,  one  sulphate  of  lime,  or 
one  baryta.  The  native  oxides  have  the  same  composition  as  the 
artificial.  These  are  facts  which  analysis  confirms  at  every  step." 

We  now  accept  the  fact  of  constant  composition  without  a  question, 
and  forget  that  it  taxed  the  brains  and  skill  of  the  world's  best  scientists 
to  prove  it.  But  even  as  late  as  1860,  Marignac,  Professor  of  Chemistry 
at  Geneva,  could  venture  to  suggest  that  slight  variations  in  com- 
position might  exist  even  among  pure  compounds.  Therefore,  begin- 
ning at  this  time,  Stas,§  a  Belgian  chemist,  carried  out  the  most  brilliant 

*  Claude  Louis  Berthollet  (1748-1822),  Teacher  in  the  Normal  and  Polytechnic 
Schools,  Paris. 

t  Josephe  Louis  Proust  (1755-1826),  Professor  of  Chemistry,  University  of 
Madrid. 

t  See  E.  von  Meyer,  History  of  Chemistry,  pp.  174-177. 

§  Jean  Servais  Stas  (1813-1891),  Professor  of  Chemistry,  Royal  Military  School, 
Brussels,  See  Armitage,  History  of  Chemistry,  pp.  239-242. 

46 


ISOTOPES  AND  THE  LAW  OF  CONSTANT  COMPOSITION         47 

series  of  investigations  known  up  to  his  time,  partially  at  least  with 
the  intention  of  proving  or  disproving  this  law. 

While  investigating  the  composition  of  silver  chloride  Stas  first 
made  the  compound  by  heating  pure  silver  metal  in  chlorine  gas. 
The  following  figures  referring  to  this  experiment  are  taken  from  his 
notes : 

Weight  of  silver  taken,  101.519  gin. 

Weight  of  chloride  formed,  134.861  gin. 

Hence,  100  gm.  of  silver  give  132.843  gm.  of  silver  chloride. 

He  then  made  the  chloride  by  dissolving  the  silver  in  nitric  acid 
and  precipitating  with  hydrochloric  acid.  By  this  method  he  obtained 
the  following  results : 

Silver  'taken  299.651  gm. 

Chloride  formed,  530.920  gm. 

From  this  we  calculate  that  100  gm.  of  silver  give  132.846  gm.  of  silver 
chloride.  The  result  here  differs  from  the  first  by  only  0.003  per  cent. 

After  completing  this  and  a  large  number  of  similar  experiments, 
Stas  stated  his  conclusion  in  the  following  words:  "  If  the  recognized 
constancy  of  stable  chemical  compounds  has  needed  further  demon- 
stration, I  consider  the  almost  absolute  identity  of  my  results  has  now 
completely  proved  it." 

In  recent  times,  T.  W.  Richards  *  of  Harvard  University  has  been 
engaged  in  a  most  splendid  series  of  researches  on  atomic  weights, 
having  at  the  same  time  in  mind  the  validity  of  the  law  of  constant 
composition.  In  a  most  careful  revision  of  the  atomic  weight  of  silver, 
he  repeated  Stas'  work  on  the  syntheses  of  silver  chloride,  employing 
even  further  precautions  than  did  Stas  himself.  He  found  as  the  aver- 
age of  a  closely  concordant  series  of  results  that  100  gm.  of  pure  silver 
gave  132.861  gm.  of  silver  chloride. 

In  a  somewhat  earlier  research  on  the  atomic  weight  of  copper,  f 
Richards  sums  up  his  conclusions  in  the  following  words:  "Another 
and  still  more  positive  conclusion  reached  by  these  results  is  that  the 
atomic  weight  of  copper  is  a  constant  quantity  with  reference  to  nitric 
acid  and  silver.  If  copper  had  a  variable  atomic  weight  it  would 
surely  appear  in  specimens  taken  from  such  widely  different  sources  " 
(viz.,  Germany  and  Lake  Superior). 

Isotopes  and  the  Law  of  Constant  Composition. — In  some  recent 
work  Richards  t  has  made  a  careful  study  of  lead  occurring  in  uranium 

*  Jour.  Am.  Chem.  Soc.,  27,  459. 

t  Proc.  Am.  Acad.  Arts  and  Sci.,  23,  180  (1887-8). 

i  Jour.  Am.  Chem.  Soc.,  38,  2613. 


48      THE  QUANTITATIVE  LAWS  OF  CHEMICAL  COMBINATIONS 

minerals,  and  has  found  the  atomic  weight  of  such  lead  to  be  only 
slightly  above  206,  while  that  of  common  lead  is  207.  This  means, 
of  course,  that  a  compound  of  this  kind  of  lead  would  contain  less  lead 
than  one  of  the  ordinary  sort.  It  should  be  understood  that  the  greatest 
pains  were  taken  to  purify  the  material,  and  the  most  careful  tests 
were  made  to  prove  the  absence  of  other  elements.  There  is  no  doubt, 
therefore,  about  the  correctness  of  the  conclusion. 

Again,  Soddy  and  Hoyman,*  working  on  lead  coming  from  thorium 
minerals,  obtained  a  value  for  the  atomic  weight  slightly  above  208. 
Here  also  the  greatest  care  was  taken  to  insure  purity  of  material, 
making  it  practically  certain  that  lead  compounds  made  from  this 
variety  of  lead  contain  more  lead  then  those  of  common  occurrence. 

More  recently,  Harkins  f  has  worked  along  this  line.  He  believes 
he  has  been  able  by  diffusion  methods  to  separate  chlorine  into  two 
forms,  one  with  atomic  weight  of  35,  the  other  with  an  atomic  weight 
of  37.  Compounds  of  either  form  of  chlorine  would  obviously  con- 
tain different  amounts  of  chlorine  than  those  we  ordinarily  deal  with. 

Still  other  elements  J  are  known,  which  show  these  different  weight 
relations,  and  further  work  is  in  progress  which  will  probably  reveal 
many  more. 

It  should  be  noted  that  the  chemical  properties  of  these  forms  of 
the  elements  having  slightly  different  atomic  weights  are  exactly  iden- 
tical. They  give  identical  spectra;  their  compounds  have  the  same 
color,  the  same  solubility ;  they  are  exactly  alike  in  every  way  excepting 
in  the  matter  of  weight.  Because  of  these  identical  properties  these 
forms  must  be  put  in  the  same  place  in  the  Periodic  System,  and  for 
that  reason  they  have  been  named  "  isotopes,"  the  word  meaning,  by 
derivation,  "  equally  placed."  Because  of  their  identical  nature,  also, 
the  compounds  of  isotopes  cannot  be  separated  by  chemical  means. 
If  mixed  by  nature  they  always  remain  so.  Ordinary  lead,  for  example, 
seems  to  be  a  mixture  of  two  isotopic  forms  occurring  in  something 
like  equal  proportions,  and,  therefore,  always  giving  an  atomic  weight 
of  about  207.  The  same  thing  is  true  of  ordinary  chlorine.  Once 
mixed,  the  two  forms  so  exactly  identical  in  chemical  properties,  go 
through  any  number  v  f  transformations  from  compound  to  compound, 
and  remain  in  exactly  the  same  relative  proportions; 

Now,  as  to  the  bearing  of  the  above  data  upon  the  validity  of  the 

*Jour.  Chem.  Soc.,  105,  1402.  [Frederick  Soddy  (1877-  ),  Professor  of 
Radio  Chemistry,  Oxford  University.] 

t  Science,  Mar.  19,  1920.  [William  Draper  Harkins  (1877-  ),  Professor  of 
Chemistry,  University  of  Chicago.] 

J  See  Washburn,  Physical  Chemistry,  pp.  20,  460. 


COMBINING  WEIGHTS  AND  RECIPROCAL  PROPORTIONS        49 

law  of  constant  composition — must  we  discard  the  law  as  no  longer 
true  to  the  facts?  Obviously  not.  If  we  continue  to  regard  the  iso- 
topes of  a  given  element  as  identical  elements  we  must,  of  course,  enlarge 
the  scope  of  the  law;  but  that  does  not  mean  that  we  must  discard  it. 
If  we  give  these  different  isotopes  different  names,  as  might  well  be 
done,  then  the  law  does  not  even  need  modification.  Any  given  com- 
pound of  a  given  isotope  will  always  have  the  same  composition,  and 
that  is  all  that  is  required  to  make  the  law  applicable.  We  shall  find 
as  we  proceed  that  many  of  the  so-called  laws  have  to  be  modified  or 
extended  to  cover  the  facts;  but  we  shall  also  find  that  very  few  of  them 
have  to  be  discarded  as  useless.  The  discovery  of  isotopes  need  not 
be  regarded  as  affecting  the  law  of  constant  composition,  except  to 
make  us  a  little  more  careful  about  the  definition. 

Combining  Weights  and  Reciprocal  Proportions. — In  studying  the 
law  of  constant  composition  we  found  that  any  given  compound  always 
contains  the  same  elements  combined  in  the  same  proportions  by 
weight.  Thus,  silver  oxide  always  contains  silver  and  oxygen  com- 
bined in  the  proportions  of  93.1  per  silver  to  6.9  per  cent  oxygen;  silver 
chloride  contains  silver  and  chlorine  combined  in  the  proportions  of 
75.26  per  cent  silver  to  24.74  per  cent  chlorine;  sodium  chloride  con- 
tains sodium  and  chlorine  in  the  proportions  of  39.33  per  cent  sodium 
to  60.67  per  cent  chlorine;  while  sodium  oxide  contains  sodium  74.19 
per  cent  and  oxygen  25.81  per  cent. 

We  might  in  this  way  go  through  the  whole  list  of  many  thousand 
compounds  made  by  reciprocal  combination  among  the  eighty  odd 
elements,  and  we  should  always  find  these  same  definite  weight  rela- 
tions. It  will  be  noted  at  once,  however,  that  each  pair  of  values 
seems  to  be  entirely  independent :  no  interrelations  can  be  seen.  Push- 
ing our  study  further,  we  shall,  nevertheless,  find  hidden  under  these 
percentage  values  an  important  law.  This  law  appears  when  we  select 
a  definite  weight  of  one  element  as  a  standard,  and  recalculate  the  other 
values  to  correspond,  keeping  the  same  proportions  as  are  indicated 
by  the  percentages.  Suppose,  for  example,  we  take  8  gm.  of  oxygen 
as  a  standard  of  comparison.  This  may  be  called  the  "  combining 
weight  "  of  oxygen.  In  silver  oxide  we  shall  find  8  gm.  of  oxygen 
combined  with  107.88  gm.  of  silver.  The  latter  value  is  then  the 
combining  weight  of  silver.  In  silver  chloride  we  find  107.88 
gm.  of  silver  combined  with  35.46  gm.  of  chlorine.  In  sodium 
chloride  we  find  35.46  gm.  of  chlorine  combined  with  23  gm.  of 
sodium.  Finally,  in  sodium  oxide  we  find  23  gm.  of  sodium  com- 
bined with  8  gm.  of  oxygen.  Note  that  by  proceeding  thus  step  by 
step  and  keeping  the  combining  weight  first  calculated  for  each  element 


Oxygen  8 


Sodium  23 


Silver  107.88 


Chlorine  35.46 

FIG.  4. — Reciprocal  Proportions. 


50      THE  QUANTITATIVE  LAWS  OF  CHEMICAL  COMBINATION 

we  have  finally  come  back  to  the  original  value  for  oxygen.  More- 
over, if  we  were  to  study  the  weight  relations  of  these  same  elements 
still  further,  we  should  find  that  oxygen  and  chlorine  also  combine 
in  the  proportions  of  8  to  35.46;  and  although  silver  and  sodium  do 
not  combine,  sodium  will  displace  silver  from  any  of  its  compounds 
in  the  proportion  of  23  to  107.88.  This  interrelationship,  is  shown 
graphically  in  Fig.  4. 

The  important  thing  to  note  here  is  that  the  porportions  in  which 
any  two  elements  react  with  a  given  element  are  also  the  proportions 

in  which  they  react  with  each 
other.  No  matter  how  far  we  carried 
our  study,  we  should  always  find 
the  elements  treating  each  other 
in  this  same  fair  and  impartial  way. 
They  seem,  as  it  were,  to  be  done 
up  in  packages,  and  thus  to  dole 
themselves  out  in  standard  amounts, 
no  matter  when  or  to  whom.  These 
facts  give  us  what  we  call  the  "  Law  of  Reciprocal  Proportions." 

The  weights  we  have  used  above  have  been  called  "  combining 
weights  "  because  they  show  the  actual  proportions  in  which  the  given 
elements  combine  with,  or  replace,  each  other.  They  are  also  quite 
frequently  called  "  equivalent  weights "  because  they  are  equivalent 
to  each  other  chemically,  one  being  able  to  take  the  place  of  the  other, 
for  example. 

For  the  first  clear  formulation  of  the  law  of  combining  weights 
and  reciprocal  proportions  we  are  indebted  to  Berzelius,*  a  Swedish 
chemist.  The  German  chemist,  Bichter,  had  performed  some  experi- 
ments along  this  line,  but  he  did  not  fully  appreciate  their  sig- 
nificance. Berzelius  began  this  work  in  1810,  and  continued  active 
along  this  line  for  at  least  eighteen  years.  Considering  his  poor  equip- 
ment, his  work  was  a  marvel  of  accuracy.  Later  workers,  like  Stas 
and  Richards,  have  added  greatly  to  the  refinement  of  his  methods. 
Their  work  has  already  been  mentioned.  We  should  also  mention  the 
great  work  of  Edward  W.  Morley,  formerly  Professor  of  Chemistry 
at  Western  Reserve  University,  who  worked  for  years  on  the  combining 
ratio  of  hydrogen  and  oxygen,  f  His  work  has  never  been  surpassed. 
The  Standard  for  Equivalent  Weights. — The  actual  values  assigned 

*  Jons  Jacob  Berzelius  (1779-1848),  Professor  of  Chemistry,  School  of  Medicine, 
Stockholm.  Great  organizer  of  chemical  science.  See  Armitage,  History  of  Chem- 
istry, p.  79. 

f  Smithsonian  Contributions  to  Knowledge,  No.  980   (1895). 


DETERMINATION  OF  EQUIVALENT  WEIGHTS  51 

to  these  equivalent  weights  were  obtained  by  the  use  of  a  perfectly 
arbitrary  standard  (8  gm.  of  oxygen).  We  might  have  used  any  other 
standard,  for  example,  100  gm.  of  oxygen  or  10  gm.  of  chlorine;  but  this 
would  not  have  changed  in  any  way  the  relation  between  the  values. 
If  under  one  system  a  certain  equivalent  weight  is  ten  times  another 
equivalent  weight  it  would  be  so  under  any  other  system.  Indeed, 
other  systems  have  been  used,  but  they  have  been  discarded  for  the 
sake  of  convenience,  and  the  one  here  suggested  is  now  the  only  one 
in  common  use.  Under  our  present  system  the  smallest  equivalent 
weight,  that  of  hydrogen,  is  1.008,  and  the  largest,  that  of  thallium, 
is  204.  Under  any  other  system,  either  hydrogen  would  be  fractional 
or  some  of  the  values  would  be  too  large  for  convenience.  As  we  shall 
see  later,  the  present  system  also  fits  into  the  current  systems  of  atomic 
and  molecular  weights. 

Gram-equivalent  Weights. — We  have  stated  our  equivalent  weights 
in  grams.  In  this  form  they  are  called  "  gram-equivalent  weights." 
They  might  have  been  stated  in  any  other  units  or  simply  as  abstract 
numbers.  The  method  we  have  employed,  however,  seems  to  give 
them  a  more  tangible  quality. 

Determination  of  Equivalent  Weights. — We  may  sum  up  our  reason- 
ing by  defining  an  equivalent  weight  as  that  weight  of  an  element  which 
will  react  with  8  gm.  of  oxygen  or  an  equivalent  weight  of  any  other 
element.  With  this  in  mind  we  find  that  there  are  evidently  two 
methods  of  determining  equivalent  weights:  First,  we  may  take  a 
known  weight  of  some  elementary  substance  and  find  the  weight  of 
oxygen  with  which  it  will  combine.  We  then  have  the  necessary 
data  for  calculating  the  weight  of  this  element  which  will  combine 
with  8  gms.  of  oxygen.  Second,  we  may  cause  a  known  weight  of 
the  element  to  combine  with,  or  displace,  some  other  element  whose 
equivalent  weight  is  known.  Taking  care  to  observe  what  weight 
of  this  second  element  is  thus  combined  or  displaced,  we  again  have 
the  necessary  data  for  calculating  the  equivalent  weight.  Combination 
with  oxygen  is  a  very  accurate  method  because  it  is  direct,  but  an  indi- 
rect method  like  the  displacement  of  hydrogen  is  often  more  convenient. 

The  Law  of  Multiple  Proportions.— The  study  of  the  laws  of  com- 
bination very  soon  developed  the  fact  that  the  same  elements  may 
unite  in  more  than  one  proportion  to  form  different  compounds.  Thus 
copper  and  oxygen  unite  in  the  proportion  of  79.9  per  cent  copper  and 
20.1  per  cent  oxygen  to  form  black  cupric  oxide,  and  in  the  proportions 
of  88.8  per  cent  copper  and  11.2  per  cent  oxygen  to  form  red  cuprous 
oxide.  Here  again  as  in  the  case  of  the  reciprocal  proportions,  the 
percentage  values  hide  the  law.  If  we  fix  the  weight  of  one  element, 


52     THE  QUANTITATIVE   LAWS   OF  CHEMICAL  COMBINATION 

and  find  what  weight  of  the  other  is  combined  with  it,  the  law  will 
appear.  Thus  the  percentage  values  may  be  taken  to  mean,  in  the  first 
case,  that  20.1  gm.  of  oxygen  are  combined  with  79.9  gm.  of  copper, 
and  in  the  second  case,  that  11.2  gm.  of  oxygen  are  combined  with 
88.8  gm.  of  copper.  If  we  keep  the  same  weight  of  oxygen  in  the  second 
case  as  in  the  first  (20.1  gm.),  we  find  by  proportion  that  20.1  gm.  of 
oxygen  are  here  combined  with  159.8  gm.  of  copper,  an  amount  exactly 
twice  as  great  as  was  present  in  the  first  case.  If  we  were  to  examine 
a  large  number  of  cases  where  the  same  elements  unite  in  different 
proportions  to  form  different  compounds  we  should  in  every  case  find 
these  simple  ratios;  the  different  weights  of  one  element  combining  with 
one  and  the  same  weight  of  another  are  always  in  the  proportion  of  small 
whole  numbers,  for  example,  1:2,  2:3,  3:5.  This  is  the  Law  of 
Multiple  Proportions. 

The  law  of  multiple  proportions  appears  to  best  advantage,  perhaps, 
if  we  translate  our  data  into  terms  or  equivalent  weights.  Thus,  in 
black  cupric  oxide,  31.8  gm.  of  copper  are  combined  with  8  gm.  of  oxygen, 
and  in  red  cuprous  oxide  63.8  gm.  of  copper  are  combined  with  8  gm. 
of  oxygen.  These  are  the  equivalent  weights  of  copper  in  the  two 
cases,  and  it  will  be  noted  at  once  that  the  second  is  exactly  twice 
the  first.  In  ferrous  compounds,  iron  has  an  equivalent  weight  of 
27.96;  in  ferric  compounds  the  equivalent  weight  is  18.63.  The  two 
equivalents  here  show  the  3  :  2  ratio. 

The  law  of  multiple  proportions  was  discovered  by  Dalton  *  in 
1803.  Dalton  was  a  coarse  experimenter,  however,  and  had  to  rely 
more  upon  the  work  of  others  for  his  data  than  upon  his  own  work. 
Berzelius  was  responsible  for  the  accurate  development  of  the  law. 
This  fact  must  not  lead  us,  however,  to  underestimate  the  value  of 
Dalton's  suggestion.  Berzelius  might  not  have  discovered  the  law 
without  it. 

The  Law  of  Combining  Volumes. — We  have  already  referred  to 
the  law  of  combining  volumes  as  the  basis  of  Avogadro's  law.  Here 
we  take  it  up  as  one  of  the  laws  of  combination.  The  volume  relations 
of  gases  are  more  simple  than  the  weight  relations.  Thus,  hydrogen 
and  oxygen  combine  in  the  rather  complicated  proportions  of  1.008  :  8 
by  weight,  while  by  volume  the  relation  is  the  very  simple  one  of  2  :  1. 
Moreover,  the  volume  of  the  product  bears  a  very  simple  relation  to 
that  of  the  reacting  gases:  where  the  volumes  of  the  reacting  gases 
are  2  :  1  that  of  the  product  is  2.  Further,  hydrogen  and  nitrogen 

*  John  Dalton  (1766-1844),  Tutor  of  Mathematics  and  Natural  Philosophy  in 
New  College,  Manchester.  Originator  of  the  atomic  theory.  See  Armitage,  His- 
tory of  Chemistry,  pp.  64-68. 


COMBINING  VOLUMES  AND  MULTIPLE  PROPORTIONS          53 

combine  3  :  1  to  form  ammonia  and  the  volume  of  the  ammonia  is  2. 
Hydrogen  and  chlorine  combine  1  :  1  to  form  hydrogen  chloride,  and 
the  volume  of  the  product  is  here  again  2.  Thus,  in  the  cases  of  all 
the  common  gases  the  combining  volumes  and  the  volumes  of  the  products 
can  be  stated  relatively  by  the  use  of  very  small  whole  numbers.  This 
fact  is  known  as  the  Law  of  Combining  Volumes. 

Combining  Volumes  and  Multiple  Proportions. — A  definite  weight 
of  carbon  combines  with  oxygen  in  two  ways.  First,  to  form  carbon 
monoxide,  a  definite  weight  of  carbon  combines  with  1  volume  of  oxygen; 
second,  to  form  carbon  dioxide  the  same  weight  of  carbon  combines 
with  2  volumes  of  oxygen.  Carbon  and  hydrogen  also  combine  in 
more  than  one  way.  Thus  to  form  ethylene  gas  a  certain  weight  of 
carbon  combines  with  1  volume  of  hydrogen,  and  to  form  methane 
the  same  weight  of  carbon  combines  with  2  volumes  of  hydrogen. 
Such  facts  as  these  remind  us  at  once  of  the  law  of  multiple  proportion; 
and,  assuming  that  a  given  volume  of  any  gas  under  the  same  conditions 
always  contains  the  same  number  of  molecules,  they  are,  no  doubt, 
illustrations  of  the  same  thing.  The  accuracy  of  correspondence 
between  the  law  of  volumes  and  the  law  of  multiple  proportions  is, 
therefore,  as  great  as  the  accuracy  of  Avogadro's  law,  and,  of  course, 
no  greater.  The  law  of  multiple  proportions  is  probably  as  exact  as 
the  law  of  constancy  of  mass;  the  law  of  volumes  would  be  exact  if 
gases  were  perfectly  ideal. 

As  a  matter  of  historical  interest  we  may  say  that  the  law  of  volumes 
was  discovered  by  Gay-Lussac.  He  saw  at  once  the  relation  between 
this  law  and  the  law  of  multiple  proportions,  and  brought  it  to  Barton's 
attention.  Dalton,  however,  never  accepted  the  validity  of  the  relation- 
ship. 

EXERCISES 

1.  What  is  the  law  of  constant  composition?     What  men  have  worked  on  it? 
Who  were  they  and  what  did  they  do? 

2.  What  is  an  isotope?     Discuss  two  cases  in  which  isotopic  forms  seem  to  con- 
stitute exceptions  to  the  law  of  constant  composition. 

3.  From  the  following  analytical  data  work  out  the  combining  weights  of  the 
given  elements  and  deduce  the  law  of  reciprocal  proportions : 

Calcium  Oxide Calcium,  71.5  per  cent;  Oxygen,  28.5  per  cent 

Calcium  Chloride Calcium,  36.1  per  cent;  Chlorine,  63.9  per  cent 

Potassium  Chloride.  .  .Potassium,  52.4  per  cent;  Chlorine,  47.6  per  cent 
Potassium  Oxide Potassium,  83  per  cent;   Oxygen,  17  per  cent 

4.  Why  has  8  gm.  of  oxygen  been  chosen  as  the  standard  for  combining  weights? 

5.  Calculate  the  equivalent  (combining  weight)  of  sodium  from  the  following 


54      THE  QUANTITATIVE  LAWS  OF  CHEMICAL  COMBINATION 

data:   Wt.  of  sodium  taken,  0.385  gm.;   volume  of  hydrogen  displaced  over  water 
at  22°  C.  and  740  mm.  pressure,  216  cc. 

6.  Give  an  accurate  definition  of  the  law  of  multiple  proportions. 

7.  Ferrous  oxide  contains:  iron,  77.73  per  cent;  oxygen,  22.27  per  cent.     Ferric 
oxide  contains:  iron,  69.94  per  cent;  oxygen, 30.06  per  cent.     Show  that  these  values 
are  in  accordance  with  the  law  of  multiple  proportions. 

8.  Define  and  illustrate  the  law  of  combining  volumes. 

9.  A  mixture  of  300  cc.  of  hydrogen  and  120  cc.  of  oxygen,  both  measured  at 
100°  C.,  was  exploded.     What  was  the  volume  of  the  mixture  after  explosion  if  the 
same  temperature  and  pressure  were  maintained? 

10.  Who  was  the  first  to  accurately  develop  the  laws  of  combining  weights  and 
reciprocal  proportions?     Who  else  has  worked  on  them? 

11.  Show  by  examples  the  relationship  between  the  law  of  multiple  proportions 
and  the  law  of  volumes. 


CHAPTER  VI 
THE  ATOMIC  HYPOTHESIS  AND  ATOMIC  WEIGHTS 

Dalton's  Hypothesis. — The  atomic  hypothesis  was  first  developed 
scientifically  by  John  Dalton  *  in  1803.  Dalton  had  spent  much  time 
in  studying  gases,  or  "  elastic  fluids/'  as  he  called  them,  and  had  thought 
much  about  the  way  in  which  they  mix  with  each  other  and  dissolve 
in  water  or  other  solvents.  His  idea  of  atoms  was  at  first  simply  a 
mechanical  or  graphic  contrivance  for  explaining  these  facts.  Soon, 
however,  he  included  in  the  hypothesis  the  matter  of  chemical  combina- 
tion and  relative  weight  relations.  As  we  have  noted  before,  he  was  a 
rather  clumsy  experimenter,  and  so  relied  more  upon  the  work  of  others 
than  upon  his  own.  He  did,  however,  do  some  rough  work  on  atomic 
weights,  and  in  the  process  came  upon  the  law  of  multiple  proportions. 

Dalton's  hypothesis  was  received  with  great  enthusiasm  by  the 
scientists  of  his  time,  such  as  Gay-Lussac  and  Berzelius,  and  its  further 
development  was  due  much  more  to  them  than  to  Dalton  himself. 
We  must  give  him  full  credit,  however,  for  the  inception  of  the  correct 
idea:  this  is  all-important.  It  is  a  most  remarkable  fact  that  the  simple 
hypothesis  first  drafted  by  Dalton  has  been  used  now  in  almost  its 
original  form  for  more  than  one  hundred  years,  and  even  with  the 
immense  volume  of  modern  research  directed  upon  it,  has  needed  little 
change.  The  simple  postulates  first  made  have  been  immensely 
expanded,  it  is  true;  but  it  has  not  been  found  necessary  to  change  them 
in  any  fundamental  way. 

Dalton's  postulates  were  three  in  number,  as  follows: 

(1)  The  chemical  elements  are  composed  of  minute  indestructible  var- 
ticles  which  we  may  call  atoms. 

(2)  All  the  atoms  composing  any  one  element  are  precisely  alike,  and 
have  the  same  weight,  but  they  differ  from  those  of  any  other  element. 

(3)  Chemical  combination  between  two  elements  consists  in  the  union 
of  a  small  fixed  number  of  atoms  of  one  element  with  a  small  fixed  number 
of  atoms  of  the  other  to  form  each  and  every  particle   (molecule)   of  the 
compound. 

It  might  be  said  that  the  facts  of  radiochemistry  seem  to  have 

*  Armitage,  History  of  Chemistry,  pp.  64-69. 
55 


56  THE  ATOMIC  HYPOTHESIS  AND   ATOMIC  WEIGHTS 

disproved,  in  part  at  least,  the  postulate  of  "  indestructible  particles." 
In  defense  of  the  postulate,  however,  we  may  say  that  atoms  do  pass 
through  all  ordinary  chemical  transformations  intact;  and,  moreover, 
the  destruction  wrought  by  radioactive  elements  is  really  not  destruction 
at  all,  but  a  transformation. 

Dalton's  Hypothesis  and  the  Laws  of  Combination. — When  the 
atomic  hypothesis  has  been  accepted,  the  laws  of  combination  follow 
of  necessity,  and  are '  therefore  immediately  explained.  Take  them 
up  one  by  one  as  follows: 

(1)  The  law  of  constant  composition  is  explained  by  supposing  that 
a  given  compound  always  contains  the  same  atoms  combined  in  the 
same  relative  numbers,  and  that  these  atoms  are  invariable  in  weight. 

(2)  To  explain  the  law  of  reciprocal  proportions  we  suppose  that 
the  atoms  have  a  certain  definite  capacity  for  holding  other  atoms 
in  combination.     Thus,  if  one  atom  of  kind  A  can  hold  in  combination 
two  atoms  of  the  kind  B,  and  one  of  B  can  hold  one  of  C,  then  A  can 
hold  two  of  C.     This  means,  of  course,  that  the  weight  of. the  element 
A  which  is  equivalent  to  the  element  B  is  also  equivalent  to  the 
element  C. 

(3)  For  the  law  of  multiple  proportions  we  must  assume  that  the 
atoms  of  some  elements  have  the  capacity  to  hold  in    combination 
more  than  one  number  of  atoms  of  some  other  kind  to  form  more  than 
one  compound. 

(4)  To  explain  the  law  of  volumes  we  must  combine  the  hypothesis 
of  atoms  with  a  correct   interpretation  of  Avogadro's  law,  and  must 
assume  that  the  ordinary  gases  are  diatomic.     The  following  example 
will  make  this  clear:    One  volume  of  nitrogen  combines  with  three 
volumes  of  hydrogen  to  produce  two  volumes  of  ammonia.     According 
to  Avogadro's  law  this  involves  n  molecules  of  nitrogen,  3n  molecules 
of  hydrogen  and  2n  molecules  of  ammonia.     Now,   each  ammonia 
molecule  must  contain  at  least  1  atom  of  nitrogen.     This  gives  us,  2n 
atoms  of  nitrogen  contained  in  the  2n  molecules  of  ammonia.     But 
these  2n  atoms  of  nitrogen  came  from  n  molecules  of  nitrogen;   hence 
we  are  compelled  to  assume  that  each  molecule  of  nitrogen  contained 
at  least  2  atoms. 

From  this  same  example  we  could  prove  that  hydrogen  is  also 
diatomic,  and  from  the  combining  volumes  in  water  and  hydrogen 
chloride  we  could  show  the  same  thing  for  oxygen  and  chlorine 
respectively. 

Atomic  Weights. — Having  accepted  the  hypothesis  that  atoms  exist 
and  that  those  of  any  one  kind  are  precisely  alike  in  weight  but  dif- 
ferent from  those  of  another,  the  next  business  would  naturally  be 

- 


ATOMIC  WEIGHTS  57 

the  determination  of  the  relative  weights  of  these  atoms.  From  what 
we  have  said  above  about  the  law  of  volumes  this  might  be  considered 
a  simple  task.  For  example,  it  might  be  supposed  that  since  three 
volumes  of  hydrogen  weighing  3  gms.  unite  with  one  volume  of  nitrogen 
weighing  14  gms.  the  formula  of  ammonia  must  be  NHs,  and  the  atomic 
weights  of  hydrogen  and  nitrogen  must  be  1  and  14  respectively.  But 
this  is  not  necessarily  true:  If  we  were  sure  that  the  molecules  of 
hydrogen  and  nitrogen  contained  exactly  2  atoms  each  and  no  more  we 
could  then  probably  assume  that  the  above  values  were  the  true  atomic 
weights.  If,  however,  the  molecule  of  nitrogen  contains  4  atoms 
the  volume  relations  compel  us  to  assume  that  4n  atoms  of  nitrogen 
go  into  2n  molecules  of  ammonia,  from  which  we  reason  that  the  formula 
of  ammonia  must  be  ^Hs.  This  would  make  the  atomic  weight  of 
nitrogen  7.  Thus,  it  can  be  seen  that  the  volume  and  weight  relations 
of  a  single  example  tell  us  nothing  dependable  about  the  relative  weights 
of  the  atoms  concerned. 

Dalton  paid  no  attention  to  the  law  of  volumes,  and,  of  course, 
knew  nothing  about  Avogadro's  law,  which  was  not  published  until 
1811.  He  simply  made  the  arbitrary  assumption  that  when  two 
elements  united  to  form  a  compound  they  would  unite  "  1  atom  of  A 
plus  1  atom  of  B  "  or  "  1  atom  of  A  plus  2  atoms  of  B."  The  values 
obtained  thus  were  often  wrong,  as  we  now  know;  but  they  served  as  a 
starting  point  for  further  research,  and  in  this  they  were  extremely 
valuable.  The  following  table  *  gives  some  of  Dalton's  values  cal- 
culated in  this  way.  It  will  be  noted  that  several  of  them  are  really 
molecular  weights  instead  of  atomic  weights.  Dalton  must  have 
appreciated  this  fact,  for  the  values  given  in  these  cases  include  the 
sum  of  the  atomic  weights  as  he  thought  they  occurred. 

Hydrogen 1 

Oxygen 5 . 66 

Azote  (nitrogen) 4 

Charcoal  (carbon) 4.5 

Water 6.66 

Ammonia -5 

Nitrous  gas  (NO) 9.66 

Nitrous  oxide  (N2O) 13.66 

Nitric  acid  (NO2) 15.32 

Sulphur 17 

Sulphurous  acid  (SO2) 22.66 

Sulphuric  acid  (SO8) 28.32 

Carbonic  acid  (CO») 15.8 

Oxide  of  carbon  (CO) 10.2 

*  Taken  from  Armitage,  History  of  Chemistry,  p.  66. 


58  THE  ATOMIC  HYPOTHESIS  AND  ATOMIC  WEIGHTS 

It  is  extremely  enlightening  to  deduce  the  formulas  of  the  compounds 
included  in  this  table,  since  they  show  how  Dalton  adhered  to  his 
arbitrary  standards  about  the  number  of  atoms,  and  also  show  what 
he  must  have  seen  by  implication.  The  value  for  water  is  evidently 
the  sum  of  the  values  for  hydrogen  and  oxygen;  so  his  formula  for 
water  must  have  been  HO.*  The  relative  weight  for  ammonia  is 
evidently  the  sum  of  the  weights  of  nitrogen  and  hydrogen,  and  his 
formula  must,  therefore,  have  been  NH.  The  weight  for  "  nitrous  gas  " 
is  equivalent  to  one  nitrogen  and  one  oxygen,  and  "  nitrous  oxide  "  is 
equivalent  to  two  nitrogen  and  one  oxygen,  while  that  for  "  nitric 
acid  "  is  one  nitrogen  and  two  oxygen.  It  is  evident  from  these 
values  that  Dalton  appreciated  the  compound  nature  of  his  "  atomic 
weights  "  referring  to  compounds,  and  also  that  he  saw  by  implication 
the  law  of  multiple  proportions. 

Dalton's  values  suffered  from  two  causes:  first,  from  poor  experi- 
mental work,  and  second,  from  the  lack  of  knowledge  as  to  the  number 
of  atoms  combining  in  any  given  compound.  Seeing  this,  Berzelius 
attacked  the  problem  of  manipulation,  and  came  wonderfully  near  its 
complete  solution.  His  values,  as  far  as  good  experimental  work  can 
make  them,  are  almost  as  accurate  as  those  in  use  to-day.  However, 
he  did  not  solve  the  problem  as  to  the  number  of  atoms  combining,  as  is 
seen  from  the  fact  that  some  of  his  values  are  one-half  those  now  current. 
The  following  table  gives  some  of  his  values,  f  recalculated  to  the  basis 
O  =  8.  He  used  the  standard  0=1. 

Hydrogen 1 . 06 

Nitrogen 7. 02 

Oxygen 8 . 00 

Sulphur 16.00 

Iron 53.33 

Copper 64 . 00 

Lead 207.79 

Mercury 200 . 00 

Potassium 40.00 

Atomic  Weights  from  Molecular  Weights. — Up  to  the  year  1860 
chemists  were  uncertain  about  the  matter  of  the  number  of  atoms 
contained  in  the  molecules  of  different  compounds  and,  therefore, 
could  not  determine  with  any  certainty  the  relative  atomic  weights. 

*Dalton  did  not  use  our  literal  symbols,  they  were  invented  by  Berzelius. 
Dalton  wrote  the  formula  for  water  graphically  as  O  O,  O  standing  for  the  hydro- 
gen and  O  for  the  oxygen  atom. 

t  Armitage,  History  of  Chemistry,  p.  93. 


ATOMIC  WEIGHTS  FROM  MOLECULAR  WEIGHTS  59 

At  this  time,  Cannizzaro,*  an  Italian  chemist,  showed  that  the  problem 
could  be  solved  by  basing  the  necessary  calculations  on  Avogadro's 
law.  He  held  that,  since  the  molecule  of  hydrogen  evidently  contains 
2  atoms,  we  should  make  the  single  atom  our  standard  of  comparison 
and  give  it  a  relative  value  of  1.  This  would  make  the  molecular  weight 
of  hydrogen  2,  and  would  give  us  the  same  standard  of  comparison  for 
both  atomic  and  molecular  weights.  He  then  showed  how  we  should 
apply  Avogadro's  law:  If  the  half-molecule  (one  atomic  weight)  of 
hydrogen  is  used  as  our  standard,  the  molecular  weights  of  all  com- 
pounds will  be  multiples  of  the  atomic  weight  of  hydrogen.  Each 
molecular  weight  will  also  be  the  sum  of  the  weights  of  all  the  atoms 
contained  within  it,  the  atomic  weights  being  measured  by  the  same 
standard  as  that  used  for  molecular  weights.  Out  of  a  given  molecular 
weight,  the  weight  due  to  a  single  element  will  depend  on  the  number 
of  atoms  of  that  element  present.  If  we  examine  a  large  number  of 
compounds  containing  a  given  element,  we  should  somewhere  find  one 
whose  molecule  contained  a  single  atom  of  the  element.  In  this  case  the 
part  of  the  molecular  weight  due  to  this  element  should  be  the  smallest 
possible.  The  problem,  then,  is  to  find  the  smallest  weight  of  the  given 
element  contained  in  the  molecular  weights  of  all  its  compounds.  The 
procedure  outlined  by  Cannizzaro  may  be  summed  up  in  three  short 
paragraphs,  thus: 

(1)  Take  as  many  volatile  compounds  of  the  given  element  as  can 
be  found,  and  determine  the  molecular  weight  of  each  one,   using  as  a 
basis  of  comparison  the  molecular  weight  of  hydrogen  (2).f 

(2)  Analyze  all  these  compounds   and  find  the  weight   of  the  given 
element  contained  in  each  moleculr  weight; 

(3)  Select  for  the  atomic  weight  the  smallest  weight  of  the  element 
found  in  the  molecular  weights  of  its  compounds,  provided  that  weight 
is  a  common  divisor  of  all  the  rest. 

An  example  will  make  this  procedure  clearer:  Suppose  we  wish  to 
determine  the  atomic  weight  of  carbon.  We  take  a  large  number  of 
carbon  compounds  and  determine  their  molecular  weights.  We  then 
find  by  analysis  the  carbon  content  of  each  molecular  weight.  Finally 
we  select  as  the  atomic  weight  of  carbon  the  smallest  weight  found 
and  the  one  which  is  a  common  divisor  of  all  the  rest.  The  following 
table  shows  the  sort  of  data  we  should  get : 

*  Stanislao  Cannizzaro  (1826-1910),  Professor  of  Chemistry,  University  of  Rome. 
Noted  particularly  for  the  contribution  here  outlined.  See  Thorpe's  Essays, 
p.  500. 

t  We  now  use  as  our  basis  of  comparison  02  =  32,  which  amounts  to  nearly  the 
same  thing.  (See  p.  41.) 


60 


THE  ATOMIC   HYPOTHESIS  AND  ATOMIC   WEIGHTS 


Carbon  Compound 


Molecular  Weight 


Carbon  Content 


Methane  

16 

12 

Ethane.  .  .  . 

30 

24 

Butane 

58 

48 

Methyl  chloride  

54  45 

12 

Ethyl  chloride 

64  45 

24 

Methyl  alcohol  

32 

12 

Ethyl  alcohol  

46 

24 

Butyl  alcohol 

74 

48 

Amyl  alcohol  

88 

60 

Ethyl  ether  

74 

24 

Iso-amyl  ether 

158 

120 

Acetone  

58 

36 

Acetic  acid  

60 

24 

Formic  acid 

46 

12 

Benzene  

78 

72 

Anthracene  

128 

120 

Upon  studying  the  list  of  carbon  contents  we  see  at  once  that  12  is 
the  smallest  weight  of  carbon  contained  in  any  of  the  molecular  weights, 
and  that  it  is  also  a  common  divisor  of  all  the  rest.  We  therefore  select 
12  as  the  atomic  weight  of  carbon. 

It  is,  of  course,  understood  that  the  above  list  is  too  short  to  be 
conclusive,  but  it  may  be  mentioned  that  after  an  examination  of 
150,000  carbon  compounds  not  one  has  yet  been  found  whose  molecular 
weight  contains  less  than  12  parts  of  carbon. 

This  one  example  serves  to  illustrate  the  manner  in  which  the 
approximate  value  of  the  atomic  weight  of  any  element  may  be  found 
in  those  cases  where  the  element  considered  furnishes  compounds  which 
are  gaseous,  or  which,  like  ether,  may  be  made  gaseous.  It  is  under- 
stood, of  course,  that  these  values  cannot  be  exact  when  the  molecular 
weights  from  which  they  originate  are  not  exact.  They  serve  the  all- 
important  purpose  of  completely  abolishing  the  problem  which  vexed 
chemists  for  many  years,  namely,  the  number  of  atoms  in  a  molecule. 
The  refinement  of  values  can  be  accomplished  by  other  means. 

Atomic  Weights  from  Specific  Heats. — The  applicability  of  the 
method  just  described  depends  on  the  existence  of  volatile  compounds 
in  anjr  given  case.  There  are  some  elements  which  either  give  no  vola- 
tile compounds  at  all  or  give  so  few  of  them  that  we  cannot  rely  Tipon 
the  evidence  furnished  in  fixing  the  values  of  the  atomic  weights.  In 
such  cases  we  must  resort  to  other  methods.  One  of  these  is  the  specific 
heat  method. 


EXACT  ATOMIC  WEIGHTS  61 

Before  describing  this  method  we  must  define  the  terms  we  need  to 
use:  Specific  heat  is  the  number  of  calories  required  to  raise  the  tem- 
perature of  1  gm.  of  substance  1°  Centigrade.  The  calorie,  as  already 
defined,  is  the  heat  required  to  raise  the  temperature  of  1  gm.  of  water 
1°.  The  specific  heat  of  water  is,  therefore,  1.  One  calorie  of  heat 
raises  the  temperature  of  1  gm.  of  mercury  31°.  The  heat  required  to 
raise  1  gm.  1°  (the  specific  heat)  is,  therefore,  1/31,  or  0.032  calorie. 

Specific  heat  can  be  determined  by  what  is  called  the  "  method 
of  mixtures."  A  definite  weight  of  the  solid  substance  is  heated  to  some 
definite  temperature  and  then  dropped  into  a  definite  weight  of  water 
whose  temperature  is  known.  The  temperature  of  the  water  is  then 
found  to  be  somewhat  higher  than  at  first.  Knowing  the  weight  of  the 
water  and  its  change  in  temperature,  we  at  once  calculate  the  number 
of  calories  of  heat  imparted  to  it.  We  know  also  how  much  the  tem- 
perature of  the  solid  substance  has  fallen,  and  we  know  that  all  the  heat 
gained  by  the  water  has  been  lost  by  the  solid.  Remembering  that  the 
number  of  calories  lost  by  the  solid  when  its  temperature  is  lowered  is 
the  same  as  would  be  required  to  raise  its  temperature  the  same  number 
of  degrees,  we  now  have  all  the  data  necessary  for  calculating  the 
specific  heat. 

Let  us  turn  now  to  the  specific  heat  method  for  determining  atomic 
weights:  In  1819  two  French  physicists,  Dulong  and  Petit,*  made  the 
important  discovery  that  the  product  of  the  atomic  weight  of  an  element 
and  its  specific  heat  was  nearly  a  constant.  Of  course  at  that  time  very 
few  of  the  atomic  weights  were  known  with  any  certainty;  but,  taking 
those  which  were  the  least  doubtful,  Dulong  and  Petit  were  able  to  work 
out  with  fair  accuracy  the  value  of  this  constant.  Thus,  they  deter- 
mined the  specific  heat  of  copper,  gold,  iron,  nickel,  lead,  bismuth, 
silicon,  tin,  zinc,  cobalt  and  silver;  and  using  the  atomic  weights  of 
these  elements  then  in  vogue,  they  obtained  for  the  constant  the  value 
6.25. 

In  spite  of  the  fact  that  the  relation  as  here  deduced  is  not  exact, 
it  will  be  seen  at  once  that  it  may  be  utilized  for  the  determination  of 
at  least  the  approximate  values  of  atomic  weights.  If  atomic  weight 
times  specific  heat  equals  6.25,  then  atomic  weight  equals  6.25  divided 
by  specific  heat. 

Later  work  has  shown  that  the  value  of  the  constant  should  prob- 
ably be  about  6.4  instead  of  6.25. 

Exact  Atomic  Weights. — Two  questions  now  arise:  First,  why 
should  we  go  to  the  trouble  of  determining  the  approximate  values  of 

*  Pierre  Louis  Dulong  (1785-1838),  Professor  of  Physics  at  the  Polytechnic 
School,  Paris.  Alexis  Petit  (1791-1820),  colleague  of  Dulong. 


62  THE  ATOMIC  HYPOTHESIS  AND  ATOMIC  WEIGHTS 

the  atomic  weights  if  we  cannot  use  them  as  they  are?  Second,  how 
are  the  exact  values  of  the  atomic  weights  determined?  We  have 
shown  that  both  atomic  and  equivalent  weights  are  determined  on  the 
basis  of  H  =  l  (more  exactly,  1.008).  The  equivalent  weight  of  oxygen 
on  this  basis  is  8,  while  the  atomic  weight  on  the  same  basis  is  16.  The 
reason  why  the  equivalent  weight  is  exactly  one-half  the  atomic  weight 
is  to  be  found  in  the  fact  that  the  atom  of  oxygen  is  able  to  hold  in 
combination  two  atoms  of  hydrogen,  and  so  the  amount  of  oxygen 
which  we  find  combined  with  one  atomic  weight  (or  one  equivalent 
weight)  of  hydrogen  is  one-half  an  atomic  weight,  or  8  parts.  Since  all 
the  atomic  weights  and  all  the  equivalent  weights  are  worked  out  on 
this  same  basis,  similar  relations  must  exist  in  every  case;  that  is,  an 
atom  of  an  element  must  combine,  either  with  a  single  atom  of  hydrogen, 
when  its  atomic  and  equivalent  weights  will  be  identical,  or  with  two 
atoms  of  hydrogen,  when  its  equivalent  weight  will  be  one-half  its 
atomic  weight,  or  with  three,  when  it  will  be  one-third,  etc.  In  all 
cases,  at  any  rate,  the  relation  between  atomic  and  equivalent  weight 
will  be  expressed  by  exact  whole  numbers. 

The  equivalent  weights  can  be  determined  with  extreme  accuracy, 
and  if  we  can  determine  just  what  multiple  of  the  equivalent  weight  to 
use  in  any  case,  we  can  determine  the  atomic  weights  with  the  same 
degree  of  accuracy.  Just  here  lies  the  value  of  the  approximate  atomic 
weights.  We  compare  our  exact  equivalent  weights  with  them,  and 
are  then  able  to  decide  at  once  what  multiple  of  the  equivalent  weight 
to  use.  An  example  will  make  this  clear:  The  specific  heat  of  a  metal 
is  0.112.  We  find  the  approximate  atomic  weight  of  the  element  by 
dividing  this  specific  heat  into  6.4,  obtaining  the  value  57.1.  The 
equivalent  weight  of  the  element,  which  has  been  determined  with 
great  accuracy,  is  27.95.  This  is  almost  exactly  one-half  the  approx- 
imate atomic  weight.  But  according  to  the  discussion  above  it  must 
be  exactly  one-half,  one-third,  etc.  Evidently  we  must  multiply  our 
equivalent  weight  by  exactly  2  to  obtain  the  exact  atomic  weight; 
doing  this,  we  obtain  the  value  55.9. 

From  this  example  we  at  once  see  the  value  of  the  approximate 
atomic  weights;  without  them  we  cannot  tell  what  multiple  of  the 
equivalent  weight  to  use.  In  the  above  case  the  atomic  weight  might 
have  been  27.95,  or  55.9,  or  83.85,  or  any  other  multiple  of  the  equivalent 
weight  so  far  as  we  could  tell,  had  it  not  been  for  a  knowledge  of  the 
approximate  value,  57.1. 

The  table  on  page  64  gives  the  names,  the  symbols,  and  the  atomic 
weights  of  all  the  known  elements.  It  is  to  be  understood  that  the 
work  of  redetermining  the  atomic  weights  is  still  going  on,  and  it  is 


PRESENT-DAY  WORK  IN  ATOMIC  WEIGHTS  63 

not  improbable  that  a  few  of  the  values  here  given  may  undergo  slight 
change.  Any  such  changes  will,  however,  probably  affect  only  the 
fractional  parts  of  the  values,  unless  unknown  isotopes  are  brought  to 
light.  There  is  now  no  case  in  which  the  approximate  value  is  not 
known,  and  any  change  of  the  value  will  probably  amount  only  to  a 
small  revision  here  and  there  of  the  value  for  a  combining  weight.  An 
international  committee  has  in  charge  the  business  of  correlating  all 
atomic  weight  work.  This  committee  revises  the  table  each  year  and 
thus  keeps  the  values  up  to  date.  This  is  obviously  necessary,  for  great 
confusion  would  result  if  the  scientists  of  different  nations  used,  in  their 
published  articles,  different  values  for  the  atomic  weights.  Our  table  of 
atomic  weights  was  reported  by  the  committee  for  1921. 

Present-day  Work  in  Atomic  Weights. — As  suggested  above,  present- 
day  work  in  atomic  weights  resolves  itself  mainly  into  a  more  careful 
determination  of  combining  weights.  In  doing  this  work  the  main 
difficulty  to  be  overcome  is  the  matter  of  purifying  the  materials  used. 
A  perusal  of  any  paper  on  atomic  weight  work  will  show  that  infinite 
pains  must  always  be  taken  to  insure  this  point;  and  even  the  best  work 
is  scarcely  ever  above  the  suspicion  that  here  and  there  traces  of  impuri- 
ties may  still  be  left.  If  a  compound  contains  water  of  hydration,  we 
are  never  absolutely  certain  that  every  trace  has  been  removed.  If  the 
compound  is  a  gas,  it  may  contain  traces  of  other  gases,  including  water. 
If  the  element  is  a  metal,  traces  of  other  metals  may  be  present.  The 
technique,  also,  of  carrying  out  the  actual  determination  must  be  an 
amazing  example  of  accuracy.  Weighings,  for  example,  must  always  be 
carried  to  the  fifth  decimal  place  and  must  be  corrected  to  vacuum 
standard;  matters  of  light  and  humidity  and  temperature  must  be 
carefully  regulated ;  and  no  pains  must  be  spared  at  any  point  to  make 
sure  that  the  reactions  involved  are  absolutely  complete  and  that  they 
proceed  exactly  in  accordance  with  the  proposed  course.  For  anyone 
who  wishes  to  become  acquainted  with  the  greatest  possible  refinement 
in  scientific  work,  nothing  could  be  better  than  to  study  carefully  some 
of  the  masterpieces  of  atomic  weight  work.  We  give  here  a  short  list; 
many  others  could  be  given: 

(1)  Sodium  and  Chlorine:  Richards  and  Wells,  Jour.  Am.  Chem.  Soc.,  27,  459. 

(2)  Hydrogen  and  Oxygen:    Morley,  Smithsonian  Contributions  to  Knowl- 

edge, No.  980. 

(3)  Sulphur:  Richards  and  Jones,  Jour.  Am.  Chem.  Soc.,  29,  826. 

(4)  Nitrogen:  Richards  and  Forbes,  ibid.  29,  808. 

(5)  Chlorine:  Noyes  and  Weber,  ibid.  30,  13. 

(6)  Iron:  Baxter  and  Cobb,  ibid.  33,  319. 

(7)  Mercury:  Easley  and  Brann,  ibid.  34,  133. 

(8)  Boron  and  Fluorine:  Van  Haagen  and  Smith,  Carnegie  Inst.  Pub.  No.  267. 


64  THE  ATOMIC  HYPOTHESIS   AND  ATOMIC  WEIGHTS 

TABLE  OF  ATOMIC  WEIGHTS  (1921) 


Element 

Symbol 

Atomic 
Weight 
0  =  16 

Element 

Symbol 

Atomic 
Weight 
0  =  16 

Aluminum 

Al 

27  0 

Molybdenum 

Mo 

96  0 

Antimony  
Argon  ... 

Sb 
A 

120.2 
39  88 

Neodymium.  .  .  . 
Neon  .      .  . 

Nd 

Ne 

144.3 
20  2 

Arsenic  

As 

74.96 

Nickel  

Ni 

58  68 

Barium  

Ba 

137  .  37 

Niton  

Nt 

222  4 

Bismuth 

Bi 

209  0 

Nitrogen 

N 

14  008 

Boron 

B 

10  9 

Osmium 

Os 

190  9 

Bromine  
Cadmium  
Caesium  
Calcium  

Br 
Cd 
Cs 
Ca 

79.92 
112.4 
132.81 
40.07 

Oxygen  
Palladium  
Phosphorus  
Platinum  

O 
Pd 
P 
Pt 

16.0 
106.7 
31.04 
195  2 

Carbon  ........ 
Cerium 

C 

Ce 

12.00 
140  25 

Polonium  
Potassium 

Po 
K 

(?) 
39  10 

Chlorine  
Chromium  
Cobalt 

Cl 
Cr 

Co 

35.46 
52.0 

58  97 

Praseodymium  . 
Radium  
Rhodium 

Pr 
Ra 
Rh 

140.9 
226.0 
102  9 

Columbium  .... 
Copper  
Dysprosium 

Cb 
Cu 
Dy 

93.1 
63.57 
162  5 

Rubidium  
Ruthenium  
Samarium 

Rb 
Ru 
Sm 

85.45 
101.7 
150  4 

Erbium  
Europium  
Fluorine  

Er 
Eu 
F 

167.7 
152.0 
19.0 

Scandium  
Selenium  
Silicon  

Sc 
Se 
Si 

44.1 

79.2 
28  3 

Gadolinium  .... 

Gd 

157.3 

Silver  

Ag 

107  88 

Gallium  
Germanium  .... 
Glucinum  

Ga 
Ge 
Gl 

70.1 
72.5 
9.1 

Sodium  
Strontium  
Sulphur  

Na 
Sr 

s 

23.00 
87.63 
32  06 

Gold  

Au 

197.2 

Tantalum  

Ta 

181  5 

Helium 

He 

4  00 

Tellurium 

Te 

127  5 

Holmium  

Ho 

163.5 

Terbium  

Tb 

159  2 

Hydrogen  

H 

1  008 

Thallium  

Tl 

204  0 

Indium  
Iodine 

In 
I 

114.8 
126  92 

Thorium  
Thulium 

Th 
Tm 

232.15 
169  9 

Iridium  ........ 

Ir 

193  1 

Tin  

Sn 

118  7 

Iron        

Fe 

55  84 

Titanium 

Ti 

48  1 

Krypton 

Kr 

82  92 

Tungsten 

W 

184  0 

Lanthanum  .... 
Lead  

La 
Pb 

139.0 
207  2 

Uranium  
Vanadium 

U 

v 

238.2 
51  0 

Lithium  

Li 

6.94 

Xenon  

Xe 

130  2 

Lutecium  

Lu 

175  0 

Ytterbium 

Yb 

173  5 

Magnesium  .... 
Manganese  

Mg 
Mn 

24.32 
54.93 

Yttrium  
Zinc  

Yt 
Zn 

89.33 
65  37 

Mercury  

Hg 

200.6 

Zirconium  

Zr 

90.6 

EXERCISES 


65 


EXERCISES 

1.  What  were  Dalton's  three  postulates? 

2.  Explain  the  laws  of  constant  composition,  reciprocal  proportions,  and  multiple 
proportions  in  terms  of  Dalton's  postulates. 

3.  Explain  the  law  of  volumes,  and  show  that  the  common  gases  must  be  at 
least  diatomic. 

4.  Show  that  if  nitrogen  were  tetra-atomic  and  hydrogen  diatomic  the  known 
volume  and  weight  relations  would  compel  us  to  assign  nitrogen  an  atomic  weight 
of  7.     What  bearing  does  this  have  on  the  problem  of  fixing  atomic  weights? 

6.  Prove  from  Dalton's  table  of  "  atomic  weights  "  that  his  formula  for  water 
must  have  been  HO.  Show  also  that  Dalton  knew  about  the  law  of  multiple  pro- 
portions. 

6.  Outline  Berzelius'  contribution  to  the  problem  of  atomic   weight  determina- 
tion. 

7.  Outline  and  illustrate  Cannizzaro's  method  for  fixing  .the  approximate  value 
of  an  atomic  weight. 

8.  What  exact  relationship  exists  between  atomic  weights  and  equivalent  weights? 
Show  just  why  this  is  so. 

9.  Define  "  specific  heat,"  and  show  how  approximate   atomic  weights  can  be 
determined  by  its  use. 

10.  The  following  table  gives  the  specific  heats  and   the  equivalent  weights  of 
a  few  elements.     Calculate  the  exact  atomic  weights. 


Sp.  Ht. 

Eq.  Wt. 

Lithium  

0.94 

6.94 

Calcium 

0  17 

20.03 

Cobalt  

0.107 

29.48 

Cerium  

0.045 

35.13 

11.  Show  just  wherein  lies  the  value  of  the  approximate  atomic  weights  deter- 
mined from  molecular  weights  and  specific  heats. 

12.  How  is  the  table  of  atomic  weights  kept  up  to  date? 

13.  What  are  some  of  the  problems  of  present-day  atomic  weight  work? 


CHAPTER  VII 

SYMBOLS,    FORMULAS,    AND    EQUATIONS:    CHEMICAL 
CALCULATIONS 

Significance  of  Symbols  and  Formulas. — The  qualitative  significance 
of  symbols  and  formulas  is  familiar  to  everyone  who  has  reached  this 
stage  in  his  chemical  education.  Thus,  everyone  knows  that  0  stands 
for  oxygen,  H  for  hydrogen,  and  Na  for  sodium,  and  that  H^SOi  stands 
for  sulphuric  acid.  Many  people  wrongly  use  the  symbols  in  place 
of  names,  saying,  for  example,  "  H2O  "  instead  of  "  water."  This  is  a 
use  for  which  symbols  were  never  intended  and  which,  no  doubt,  leads 
to  the  common  ignorance  of  their  real  meaning. 

The  most  important  meaning  of  a  chemical  symbol  is  a  quantitative 
one.  A  symbol  stands  for  one  atomic  weight  of  an  element.  Thus,  the 
symbol  Cu  stands  for  63.6  parts  of  copper,  Na  stands  for  23  parts  of 
sodium,  and  Pb  stands  for  207.2  parts  of  lead.  Just  as  in  the  case  of 
molecular  weights,  it  is  sometimes  convenient  to  state  atomic  weights 
in  grams.  If  so  stated,  the  symbols  stand  for  gram-atomic  weights. 

A  formula  stands  for  one  molecular  weight  of  a  compound  or  element ; 
at  the  same  time  it  shows  what  elements  and  how  many  atomic  weights 
of  each  are  combined  to  give  one  molecular  weight.  Thus,  the  formula 
CuSO4  stands  for  one  molecular  weight  of  copper  sulphate  (159.6  parts). 
It  also  stands  for  the  fact  that  one  atomic  weight  of  copper  (63.6  parts), 
one  atomic  weight  of  sulphur  (32  parts),  and  four  atomic  weights  of 
oxygen  (4X16  parts),  are  combined  to  form  one  molecular  weight  of 
sulphate. 

It  should  be  noted  that  the  molecular  weight  above  is  the  sum  of  the 
atomic  weights  contained  within  it.  Up  to  this  time  we  have  given  no 
exact  method  for  determining  molecular  weights.  We  have  shown  that 
the  metKod  based  on  Avogadro's  law  gives  only  approximate  results. 
The  fact  is  that  the  exact  molecular  weight  of  a  compound  cannot  be 
determined  until  its  formula  is  known,  and  then  the  molecular  weight 
is  determined  by  the  very  simple  method  of  adding  together  the  atomic 
weights  represented  by  the  formula. 

The  Making  of  Formulas. — If  the  compound  in  question  is  capable 
of  being  volatilized  without  decomposition  the  method  of  determining 
the  formula  is  very  simple;  it  includes  the  following  steps: 

66 


THE  MAKING  OF  FORMULAS  67 

(1)  The  molecular    weight    is    determined;  i.e.,  the  weight  of  22.4 
liters  of  the  substance  in  gaseous  form  and  under  standard  conditions. 

(2)  The  compound  is  analyzed,  in  order  to  determine  what  portion 
of  the  molecular  weight  is  to  be  assigned  to  each  element  contained  in  it, 
the  results  of  analysis  being  stated  in  the  same  units  as  the  molecular 
weights,  not  in  per  cents. 

(3)  The   results    of   analysis    are    divided    by  the  respective  atomic 
weights,  to  determine  how  many  atomic  weights  of  each  element  are  con- 
tained in  the  molecular  weight. 

(4)  These  results  are  then  stated  in  terms  of  the  chemical  symbols. 
Take  the  following  example: 

The  weight  of  22.4  liters  of  chloroform  vapor  under  standard  condi- 
tions is  119  gms.  This  is  the  molecular  weight  of  chloroform. 

Analysis  shows  that  of  this  119  gms.,  12  gms.  are  carbon,  1  gm.  is 
hydrogen,  and  106  gms.  are  chlorine. 

Dividing  by  the  respective  atomic  weights,  we  find  that  these 
amounts  consist  of  one  atomic  weight  of  carbon,  one  atomic  weight 
of  hydrogen,  and  three  atomic  weights  of  chlorine. 

Stating  these  values  in  terms  of  the  symbols  we  obtain  the  formula 
CHCls. 

There  are  substances  whose  molecular  weights  cannot  be  determined 
by  any  of  the  known  methods.  In  such  cases  we  cannot  determine  the 
true  formula  and  must  content  ourselves  with  arranging  the  symbols 
in  such  a  way  as  to  express  simply  the  correct  proportion  of  the  elements. 
Ferric  oxide  is  such  a  substance.  It  cannot  be  volatilized  or  dissolved, 
and  therefore  we  have  no  means  of  determining  what  its  molecular 
weight  is.  Analysis  of  this  substance  gives:  iron,  70  per  cent;  oxygen, 
30  per  cent.  This  gives  the  proportions  of  the  elements,  but  the  amounts 
are  not  stated  in  terms  of  the  atomic  weights,  and  therefore  cannot  be 
represented  by  the  symbols  Fe  and  0.  To  bring  the  results  of  analysis 
into  the  proper  form  we  divide  the  percentages  by  the  respective  atomic 
weights  (56  and  16).  The  result  is  1.25  atomic  weights  of  iron  and 
1.875  atomic  weights  of  oxygen,  which  we  may  write  Fe1>25  Oi.875- 
But  we  have  long  since  agreed  that  molecules  do  not  contain  parts  of 
atoms.  We  therefore  divide  the  fractional  numbers  by  their  highest 
common  factor  (0.625),  and  obtain  as  a  result  the  formula  Fe20s. 

This  is  the  simplest  formula  we  can  write  which  expresses  the  results 
of  analysis  in  terms  of  the  chemical  symbols.  The  true  formula  may 
be  Fe40e,  or  any  multiple  of  the  simple  formula.* 

Most  of  the  solid  elements,  like  copper  and  iron,  belong  to  the  class 

*  The  solid  probably  possesses  the  lattice  structure  mentioned  in  Chapter  I, 
in  which  the  unit  is  the  atom,  not  the  molecule. 


68  SYMBOLS,   FORMULAS,   AND  EQUATIONS 

whose  molecular  weights  cannot  be  determined.  Therefore  we  do  not 
know  what  their  molecular  formulas  are,  and  we  are  obliged  to  use  the 
single  symbols  for  this  purpose.  Mercury  and  silver  have  been  vapor- 
ized, and  in  this  form  the  molecules  are  monatomic.  What  they  are 
in  the  solid  or  liquid  form,  we  do  not  know.* 

The  Significance  and  Making  of  Equations. — Chemical  equations 
express  chemical  change  both  qualitatively  and  quantitatively.  If  it  is 
desired  to  have  molecular  and  volume  relations  expressed,  the  equation 
should  be  so  arranged  that  all  the  interacting  substances  and  the 
products  resulting  from  their  interaction  will  appear  as  full  molecules. 
Thus,  oxygen  should  appear  as  Cb,  hydrogen  should  appear  as  H2, 
chlorine  as  Ck,  etc.  An  equation  written  in  this  form  is  called  a 
"  molecular  equation."  In  line  with  this,  the  equation  for  the  decompo- 
sition of  mercuric  oxide  should  be  written  thus: 

2HgO  +±  2Hg+02 

This  equation  expresses  two  things:  (1)  Qualitatively,  it  shows  that 
mercuric  oxide  breaks  up  into  mercury  and  oxygen,  and  that  the  reaction 
is  reversible;  i.e.,  that  mercury  and  oxygen  also  unite  to  form  mercuric 
oxide.  It  also  shows  that  mercury  is  monatomic  and  oxygen  diatomic. 
(2)  Quantitatively,  the  equation  shows  that  two  moles  of  mercuric 
oxide  give  two  moles  of  mercury  and  one  mole  of  oxygen.  The  volume 
of  the  oxygen,  measured  under  standard  conditions,  is  22.4  liters. 

Reduced  to  its  lowest  terms,  the  process  of  writing  an  equation  is 
as  follows:  (1)  Knowing  what  substances  are  reacting,  we  must  first 
ascertain  what  substances  are  produced.  This  is  a  matter  which  we 
cannot  always  predict,  and  which  we  cannot  find  out  by  simple  inspec- 
tion. It  can  only  be  determined  by  experiment,  and  if  we  have  not  the 
data,  we  must  look  the  matter  up.  Thus,  oxygen  gas  and  metallic  iron 
are  heated  together.  Supposedly  the  product  might  be  either  F^Os 
or  Fes04;  experimentally  it  is  found  to  be  FesC^,  the  magnetic  oxide. 

(2)  We  substitute  symbols  and  formulas  for  the  names  of  the  sub- 
stances reacting  and  of  the  substances  produced.     Thus,  in  the  above 
case,  we  write: 

Fe+O2  <=±  Fe3O4 

(3)  We  balance  the  equation;  that  is,  we  arrange  to  have  the  same 
number  of  atomic  weights  of  any  given  element  on  either  side  of  our 

*Some  attempts  have  been  made  to  determine  the  formulas  of  metals  by  dissolving 
in  mercury  and  determining  the  freezing  point  of  the  solution.  The  results  are  not 
entirely  satisfactory,  but  so  far  as  they  go  they  indicate  that  the  metals  in  such 
solutions  are  monatomic. 


CALCULATIONS  INVOLVING  SYMBOLS  69 

equation.  In  other  words,  we  make  our  equation  tell  the  truth.  The 
equation  in  (2)  says  that  one  atomic  weight  of  iron  and  two  atomic 
weights  of  oxygen  unite  to  produce  one  mole  of  magnetic  oxide  con- 
taining three  atomic  weights  of  iron  and  four  of  oxygen.  This  is  evi- 
dently impossible.  Properly  balanced,  the  equation  becomes: 

3Fe+202  +±  Fe3O4 

Calculations  Involving  Symbols,  Formulas,  and  Equations.  —  What 
has  been  said  about  the  quantitative  significance  of  symbols  and  for- 
mulas should  make  it  possible  to  solve  most  chemical  problems  without 
difficulty,  provided  these  statements  are  understood.  It  is  possible, 
however,  to  give  certain  hints  as  to  general  procedure  which  will  make 
mistakes  much  less  likely  to  occur  and  which  in  many  cases  will  shorten 
the  work.  The  procedure  should  almost  always  include  the  following 
steps  : 

(1)  Write  a  molecular  equation  representing  the  change  or  molecular 
ratio. 

(2)  Place   beneath    the   symbols    their   respective   quantitative   values, 
either  in  weights  or  volumes  as  the  case  may  require. 

(3)  Arrange   the   known   value   and   the   unknown   value    (x)    under 
their  respective  symbols. 

(4)  Arrange    the    numbers    so    that    the    quantitative    values  for    the 
symbols  form  the  first  member  of  a  proportion  and  the  known  and  unknown 
values  from  the  problem  form  the  second  member. 

(5)  Solve  the  proportion. 

These  steps  may  be  illustrated  by  use  of  the  following  problems: 

(1)  What  weight  of  potassium  chloride  (KC1)  can  be  obtained  from  2.4  gms. 
of  potassium  chloroplatinate 


Step  (1)  K2PtCl6  r->  2KC1. 

Step  (2)  486.2        2X74.6     (149.2) 

Step  (3)  2.5           x 

Step  (4)  486.2  :  149.2  ::  2.5  :  x 

G,       /Kv  2.  5X149.  2  gm. 

Step  (5)  *~ 


Note  that  the  equation  contains  2KC1.  Since  the  original  salt 
contains  two  atomic  weights  of  potassium  it  is  perfectly  evident  that 
one  mole  of  it  would  give  two  moles  of  potassium  chloride,  not  one  mole. 


70  SYMBOLS,   FORMULAS,   AND  EQUATIONS 

(2)  What  volume  of  hydrogen  under  standard  conditions  would  be  obtained  by 
dissolving  10  gms.  of  aluminum  in  hydrochloric  acid? 

Step  (1)  2A1+6HC1  ->  3H2+2A1C13 

Step  (2)  2  X  27.0  gm.          3  X  22.4  liters 

Step  (3)  10  gms.  x      liters 

Step  (4)  54.2  :  67.2::  10  :  x 

10X67. 2  liters 


Step  (5)  x  = 


54.2 


Here  note  the  equation  again.  To  express  volume  properly  the 
hydrogen  must  appear  as  moles  (Ek),  each  of  which  occupies  a  volume 
of  22.4  liters.  This  necessitates  writing  the  equation  as  seen. 

Some  teachers  are  very  much  opposed  to  the  use  of  the  proportion 
(step  4),  and  would  omit  this  entirely.  They  say  that  the  "  mystic 
dots  "  are  very  confusing,  and  that  students  who  use  them  "  often 
fail  to  get  the  connection  between  proportion  and  the  ordinary  algebraic 
procedures,  and,  what  is  still  more  serious,  they  fail  to  get  its  logical 
basis."  The  author's  personal  experience  does  not  bear  out  this  criti- 
cism, but  there  is  certainly  no  objection  to  the  use  of  a  method  which 
avoids  the  form  of  the  proportion.*  To  do  this  proceed  as  follows: 

Arrange  steps  (1),  (2),  and  (3)  as  directed.  In  place  of  step  (4)  simply 
reason  out  the  solution.  For  example,  in  the  first  problem  say,  "  Since 
486.2  gms.  of  potassium  chloroplatinate. produces  149.2  gms  of  potas- 
sium chloride,  2.5  gms  will  produce  2.5/486.2  of  149.2  gms." 

In  the  second  problem  say,  "  Since  54.2  gms.  of  aluminum  produce 
67.2  liters  of  hydrogen,  10  gms.  will  produce  10/54.2  of  67.2  liters." 


EXERCISES 

1.  Give  the  qualitative  and  quantitative  significance  of  symbols;  of  formulas. 

2.  Give  a  general  method  of  procedure  for  working  out  the  formula  of  a  com- 
pound;  (a)  from  its  molecular  weight  and  analysis;   (6)  from  its  analysis  alone. 

3.  Show  by  means  of  an  example  the  steps  necessary  for  working  out  a  molec- 
ular equation. 

4.  Outline  a  general  procedure  for  the  solution  of  chemical  problems,   (a)  involv- 
ing the  form  of  a  proportion;    (6)  avoiding  the  form  of  a  proportion. 

6.  A  certain  gas  contains:  carbon,  46.1  per  cent;  nitrogen,  53.9  per  cent.  One 
liter  of  the  gas,  under  standard  conditions,  weighs  2.33  gms.  Determine  the  formula. 

6.  One  liter  of  argon  gas,  under  standard  conditions,  weighs  1.78  gms.  Is  the 
argon  molecule  monatomic,  or  diatomic? 

*  Proportion  is  really  inherent  in  the  nature  of  the  problem,  and  so  cannot  be 
avoided. 


EXERCISES  71 

7.  A  compound  contains  52.2  per  cent  carbon,   13.1  per  cent  hydrogen,  and 
34.7  per  cent  oxygen.     The  molecular  weight  is  46.     Calculate  the  formula. 

8.  One  liter  of  chlorine  gas  weighs  3.17  gms.  (at  0°  and  760  mm.).     Calculate 
the  formula. 

9.  One  volume  of  hydrogen  unites  with  1  volume  of  chlorine  to  form  2  volumes  of 
hydrogen  chloride  gas.     Prove  that  chlorine  and  hydrogen  must  be  at  least  diatomic. 

10.  Calculate  the  formula  of  the  oxide  formed  when  43.45  gms.  of  lead  unite 
with  4.48  gms.  of  oxygen. 

11.  Calculate  the  per  cent  of  CaO  in  a  sample  of  impure  calcium  carbonate  which 
yielded  43.8  per  cent  CO2,  assuming  that  all  the  CO2  was  attached  to  the  calcium. 

12.  A  sample  of  ferrous-ammonium    sulphate,  FeSO4(NH4)2SO4rcH2O,    yielded 
8.92  per  cent  NH3.     What  per  cent  of  iron  did  it  contain? 

13.  What  volume  of  CO2,  under  standard  conditions,  will  be  liberated  by  dis- 
solving 10  gms.  of  magnesium  carbonate  (MgCO3)  in  an  acid?     What  volume  will 
this  gas  occupy  at  20°  C.  and  75  cm.  pressure? 

14.  One  gm.  of  methane  (CH4),  at  100°  C.  and  760  mm.  pressure,  was  burned 
to  water  and  carbon  dioxide.     What  were  the  volumes  of  the  products  under  the 
same  conditions? 

15.  One  gm.  of  methane  was  mixed  with  5  gms.  of  oxygen,  both  gases  measured 
at  0°  C.  and  760  mm.     The  mixture  was  exploded,  and  then  brought  back  to  standard 
conditions.     What  was  the  final  volume? 

16.  Using  no  data  but  formulas,  atomic  weights,  and  molecular  volume,  calculate 
the  molar  weight  and  the  weight  of  one  liter  of  each  of  the  following  gases :  ammonia, 
hydrogen  chloride,  sulphur  dioxide,  hydrogen  sulphide,  phosgene,  phosphine,  nitrous 
oxide,  ethylene. 


CHAPTER  VIII 
CHEMICAL  VALENCE 

The  Idea  of  Valence. — The  capacity  of  an  atom  to  hold  other  atoms 
in  combination  is  called  its  "  valence."  The  atom  of  hydrogen  is 
never  found  holding  in  combination  more  than  one  atom  of  another 
element;  hence  we  say  its  valence  is  one,  or  we  sometimes  call  it  a 
"  univalent  element."  There  are  several  of  the  elements  whose  combin- 
ing capacity  is  exactly  like  that  of  hydrogen — their  individual  atoms 
combine  with  one  atom  of  hydrogen  or  take  the  place  of  one  atom  of 
hydrogen — we  therefore  call  all  these  elements  univalent.  Examples 
of  this  kind  are:  silver,  potassium,  sodium,  chlorine,  bromine,  and 
iodine.  But  there  are  some  of  the  elements  whose  individual  atoms  are 
able  to  combine  with  or  replace  two  atoms  of  hydrogen  or  of  any  other 
univalent  element:  these  elements  are  called  "  bivalent."  Examples 
of  this  class  are:  copper  (ic),  iron  (ous),  calcium,  magnesium,  barium, 
oxygen,  and  sulphur.  Besides  these  two  classes  there  are  also  trivalent 
elements,  like  ferric  iron,  chromium,  aluminum,  and  tetravalent  ele- 
ments, like  stannic  tin,  carbon,  etc.  Finally,  there  are  those  of  higher 
valence,  up  to  eight,  which  seems  to  be  the  limit. 

We  have  shown  that  in  those  cases  where  the  atom  of  an  element 
can  hold  in  combination  only  one  atom  of  hydrogen  the  equivalent  is 
identical  with  the  atomic  weight,  while  in  those  cases  where  the  atom 
combines  with  more  than  one  atom  of  hydrogen  the  equivalent  weight 
is  one-half,  one-third,  etc.,  of  the  atomic  weight,  depending  on  the 
number  of  hydrogen  atoms  held  in  combination.  We  note  at  once 
that  those  elements  whose  atomic  and  equivalent  weights  are  identical 
are  univalent  elements,  those  whose  equivalent  weight  is  one-half  the 
atomic  weight  are  bivalent  elements,  those  whose  equivalent  weight  is 
one-third  are  trivalent  elements,  etc.  Numerically,  then,  we  see  that 
the  valence  of  an  element  is  the  same  as  the  number  of  equivalents  in 
the  atomic  weight.  The  following  examples  will  show  this:  One  atom 
of  chlorine,  Cl,  unites  with  one  H  to  form  HC1,  and  both  the  equivalent 
weight  and  the  atomic  weight  of  chlorine  are  35.46.  Chlorine  is  also 
a  univalent  element.  One  atom  of  oxygen,  O,  combines  with  2H  to 
form  H2O,  and  the  atomic  weight  of  oxygen  is  twice  its  equivalent 
weight.  Oxygen  is  also  a  bivalent  element. 

72 


VARIABILITY  OF  VALENCE  73 

Variability  of  Valence. — As  implied  in  the  above  discussion,  the 
valence  of  an  element  is  not  always  the  same.  The  same  thing  is 
implied  also  in  the  law  of  multiple  proportions  where  an  element  has 
more  than  one  equivalent  weight.  In  fact,  there  are  only  a  few  of  the 
elements  which  do  not  show  more  than  one  valence.  The  alkali  metals 
— lithium,  sodium,  potassium,  rubidium,  and  caesium — are  probably 
always  univalent;  and  the  alkaline  earths — calcium,  barium,  strontium, 
and  magnesium — are  probably  always  bivalent;  but  there  are  few  others 
which  do  not  appear  sometimes  with  one  valence  and  sometimes  with 
another.  Thus,  chlorine  is  usually  univalent,  as  in  HC1  or  CCLt,  but  it 
also  functions  as  trivalent  in  HClCb,  as  pentavalent  in  HClOs,  and  as 
heptavalent  in  HCICU.  Nitrogen  is  trivalent  in  NHa  and  pentavalent 
in  N2O5  or  HNOs-  Carbon  is  usually  tetravalent,  as  in  CH*  or  CC>2, 
and  the  organic  chemists  are  inclined  to  regard  it  as  always  so.  Indeed, 
they  regard  tetravalent  carbon  as  the  bed  rock  of  their  whole  system, 
although  it  certainly  seems  to  be  bivalent  in  CO.  Iron  is  bivalent 
in  ferrous  compounds  and  trivalent  in  ferric.  Copper  is  univalent  in 
cuprous  compounds  and  bivalent  in  cupric.  Sulphur  is  bivalent  in 
H2S,  trivalent  in  8203,  tetravalent  in  862,  and  hexavalent  in  80s  or 
H2SO4.  N 

We  might  thus  continue  to  present  examples,  and  should  find  the 
number  almost  endless;  but  the  above  are  quite  sufficient  to  show  that 
valence  is  often  a  variable  thing. 

We  must  note  in  passing  that,  in  spite  of  its  variability,  the  valence 
of  an  element  is  very  fundamental,  and  the  change  from  one  valence  to 
another  is  no  light  matter.  Thus,  copper  with  a  valence  of  one  is 
very  much  like  silver:  its  salts  are  white  in  color;  they  are  insoluble  in 
water,  soluble  in  ammonia.  Copper  with  a  valence  of  two  is  like 
nickel:  its  salts  are  green  or  blue;  they  are  easily  soluble  in  water;  they 
form  blue  complexes  with  ammonia.  Many  examples  like  this  could 
be  given,  showing  that  an  element  functioning  under  different  valences 
is  often  as  different  as  two  distinct  elements. 

Valence  and  Structural  Formulas. — The  valence  of  an  element  may 
usually,  be  seen  by  inspection  of  the  formulas  of  compounds  where 
the  element  is  found  in  combination  with  some  other  element  of  known 
valence.  Thus  we  are  fairly  safe  in  saying  that  the  formula  TaCls 
gives  tantalum  a  valence  of  five,  and  that  the  formula  MgCk  gives 
magnesium  a  valence  of  two.  This  is  not  a  safe  general  rule  to 
follow,  however,  for  we  should  thus  be  led  into  some  strange  situa- 
tions. For  example,  we  should  have  to  say  that  sodium,  in  NaNs, 
had  a  valence  of  nine,  if  nitrogen  is  trivalent,  and  we  might  imagine 
that  hydrogen  in  H2O2  was  bivalent.  What  we  need  for  a  safe  guide 


74  CHEMICAL  VALENCE 

is  the  so-called  "  structural  formula  "  of  a  compound,  properly  arranged 
by  someone  who  knew  beforehand  the  valences  of  the  elements  con- 
cerned. Thus  the  formula  of  sodium  nitride  given  above  would  become, 
when  structurally  written, 

/N 
.         •  Na-N<||  . 

Here  the  valence  of  the  sodium  is  clearly  seen  to  be  one,  as  usual. 
Again,  from  the  formula  H2SO4  we  might  reason  that  sulphur,  combined 
with  64  and  H2,  must  have  a  valence  of  ten;  but  the  use  of  a  properly 
arranged  structural  formula  clears  up  the  case  at  once.  The  accepted 
structural  formula  for  sulphuric  acid  is 

H 
H 

Here  it  is  plainly  seen  that  the  sulphur  has  a  valence  of  six,  and  that 
the  hydrogen  is  not  combined  with  the  sulphur  at  all. 

The  lines  drawn  between  symbols  in  structural  formulas  to  represent 
valences  are  sometimes  called  "  bonds."  Each  bond  represents  a  single 
valence,  and  by  counting  the  number  radiating  out  from  any  given 
symbol  we  arrive  at  the  valence  of  the  element  represented.  Bonds 
are  much  used  in  organic  chemistry,  where  the  ideas  of  valence  and 
structure  relations  are  most  highly  developed. 

We  must  not  leave  the  subject  of  structural  formulas  without  a 
word  of  caution.  It  must  not  be  gathered  from  what  has  been  said 
that  structural  formulas  are  arranged  solely  with  reference  to  the 
matter  of  valence.  They  are  expected,  first  of  all,  to  be  faithful  to  the 
known  chemical  properties  of  the  compounds  concerned.  That  they 
express  valence  also  is  mainly  incidental.  Take  a  few  examples: 
The  structural  formula  for  common  alcohol  is 

H     H 

H— C— C— OH 

I       I 
H    H 

It  has  been  proved  by  careful  experiments  that  the  molecule  of  alcohol 
contains  two  carbon  atoms,  that  these  two  atoms  are  attached  to  each 
other;  that  one  carbon  atom  has  three  hydrogen  atoms  attached  to  it 
and  that  the  other  has  two,  and  finally  that  the  molecule  contains  a 


POSITIVE  AND  NEGATIVE  VALENCE  75 

hydroxyl  group  attached  to  a  carbon  atom.  The  formula  shows  all 
this.  At  the  same  time  it  shows  that  carbon  is  tetravalent  in  both 
cases.  The  structure  of  the  formaldehyde  molecule  is  represented  thus : 

H 
H 

It  is  not  represented  by  the  formula  H — C — OH,  for  it  does  not  contain 
hydroxyl.  This  is  more  important  than  the  fact  that  it  makes  carbon 
bivalent,  which  it  might  possibly  be.  Acetic  acid  is  represented  cor- 
rectly by  the  formula 

H 

I         >> 
H—  C— Cf 
|        N)H 
H 

Preparation  and  chemical  behavior  indicate  that  the  molecule  contains 
just  what  the  formula  represents,  including  the  carbonyl  group,  C  =  O, 
and  the  hydroxyl  group,  OH,  attached  as  indicated.  Incidentally  the 
valence  of  each  element  is  also  indicated. 

Positive  and  Negative  Valence. — Thus  far  we  have  spoken  of 
valence  simply  as  a  number  or  capacity,  indicated,  for  example,  by  one 
bond,  two  bonds,  etc.  It  is  evidently  important,  however,  to  observe 
whether  the  element  concerned  is  acting  in  a  positive  capacity  or  in  a 
negative  capacity.  H  in  HC1  is  certainly  positive,  for  it  is  attracted 
to  the  negative  electrode  during  electrolysis;  and  Cl  is  here  certainly 
negative  because  it  is  attracted  to  the  positive  electrode.  Where  an 
element  is  acting  in  a  positive  capacity,  like  hydrogen  in  HC1,  we  say  it 
has  positive  valence,  and  where  it  is  acting  in  a  negative  capacity, 
like  Cl  in  HC1,  we  say  it  has  negative  valence.  Positive  and  negative 
valence  are  indicated  by  the  proper  signs,  +  and  — ,  and  the  number 
of  the  signs  used  in  any  case  indicates  the  numerical  value  of  the  valence. 
Thus,  in  the  above  case,  hydrogen  is  univalent  positive,  indicated  by 
H+,  and  chlorine  is  univalent  negative,  indicated  by  Cl~.  Aluminum 
is  trivalent  positive,  as  indicated  by  the  symbol  A1+  ++,  and  sulphur 
in  H2$  is  bivalent  negative,  indicated  by  the  symbol  S=. 

An  important  fact  to  remember  in  connection  with  positive  and 
negative  valence  is  that  the  same  element  may  act  in  either  capacity. 
Nitrogen  in  NH3  seems  to  be  trivalent  negative  as  indicated  by  the 
structural  formula 

/H+ 
- 


76  CHEMICAL  VALENCE. 

In  HN03  nitrogen  seems  to  be  pentavalent  positive  as  indicated  in  the 
formula 

HO—  N+/ 
+^ 


Chlorine  in  HC1  is  univalent  negative,  and  chlorine  in  HC1O4  is  hep- 
tavalent  positive,  thus: 


The  case  of  the  elementary  gases  is  interesting.  We  have  already  seen 
that  these  gases  are  diatomic,  and  we  write  the  formulas  as  Cfe,  02,  H2, 
12,  etc.  To  account  for  the  combination  of  the  two  atoms  of  the  same 
element  it  is  sometimes  assumed  that  one  atom  is  positive  and  the 
other  negative,  thus:  C1+C1",  H+H~,  O+O,  etc.  In  favor  of  this 
assumption  the  following  experimental  evidence  is  advanced:  When 
iodine  is  heated  to  very  high  temperatures  it  becomes  monatomic  and 
at  the  same  time  becomes  a  conductor  of  electricity.*  The  latter  fact 
is  understood  to  indicate  the  presence  of  positive  and  negative  iodine 

*  J.  J.  Thomson,   Corpuscular  Theory  of  Matter,  p.  130,  also  Walden,  Zeitschr. 
physikal.  Chemie,  43,  385. 


HO-C1+     =0 

So 

Carbon  in  methane  seems  to  be  tetravalent  negative,  thus: 

H+ 

H+—  C^—  H+ 

I 
H+ 

• 

but  carbon  in  C  CU  seems  to  be  tetravalent  positive,  as  also  in  CO2,  thus: 

ci-  + 

+  + 

+  + 

C1-—  C—  Cl-     and    O="=C+=a= 


POSITIVE  AND  NEGATIVE  VALENCE  77 

atoms.  If  these  atoms  did  not  assume  their  opposite  charges  at  the 
instant  of  separation  they  must  have  been  thus  charged  when  in  com- 
bination. Another  example  is  the  following:  A  platinum  wire  passing 
through  a  bulb  filled  with  air  is  heated  to  redness  by  passage  of  the 
electric  current.  Hydrogen  gas  is  then  substituted  for  the  air,  where- 
upon the  wire  ceases  to  glow  unless  the  current  is  increased.  The 
heat  from  the  wire  dissociates  the  hydrogen  molecules  in  its  immediate 
neighborhood,  and  the  separate  atoms  thus  produced  carry  a  part 
of  the  current,  thus  lessening  the  current  in  the  wire.  These  atoms 
could  not  carry  the  current  if  they  were  not  oppositely  charged.* 

In  either  of  these  cases  there  is  probably  no  question  about  the 
opposite  charges  on  the  separate  atoms;  but  the  weakness  of  the  argu- 
ment lies  in  assuming  that  the  atoms  were  necessarily  thus  charged  when 
combined.  In  a  later  chapter  (Atomic  Structure)  we  shall  discuss  a 
theory  which  seems  to  make  this  assumption  unnecessary. 

The  strangest  fact  connected  with  this  matter  of  positive  and 
negative  valence  is  that  in  certain  cases  the  same  atom  seems  to  be 
able  to  function  in  both  ways  at  once.  Take  the  case  of  the  carbon 
atom  in  chloroform.  The  structural  formula  for  chloroform  is 


As  far  as  we  know,  hydrogen  always  acts  as  a  positive  element  when 
in  combination  with  other  elements.  Chlorine  seems  to  act  sometimes 
as  a  positive  element  and  sometimes  as  negative.  If  the  hydrogen  is 
positive  and  the  chlorine  negative  in  the  chloroform  molecule,  then  the 
carbon  atom  is  univalent  negative  and  trivalent  positive.  That  the 
chlorine  is  negative  seems  to  be  proved  by  the  fact  that  chloroform 
with  NaOH  yields  NaCl,  in  which  Cl  is  surely  negative.  It  should  be 
noted,  however,  that  this  case  is  also  covered  by  the  theory  mentioned 
in  the  last  paragraph. 

One  more  fact  must  be  noted  before  leaving  this  subject  of  positive 
and  negative  valence.  A  careful  study  will  show  that  in  many  cases 
the  sum  of  the  maximum  positive  and  negative  valences  of  an  element  is 
eight.  Take  the  following  examples: 

*  The  lowering  of  the  temperature  may  in  part  be  due  simply  to  the  fact  that 
the  hydrogen  atoms  produced  by  dissociation  diffuse  away  rapidly,  carrying  off 
the  heat.  See  Langmuir,  Jour.  Am.  Chem.  Soc.,  37,  417. 


78  CHEMICAL   VALENCE 

C  in  CO2+4,  in  CH4-4,  sum  8. 

N  in  N205+5,  in  NH3-3,  sum  8. 

S  in  SO3+6,  in  H2S-2,  sum  8. 

Cl  in  HClO4+7,  in  HC1-1,  sum  8. 

Os  in  OsO4+8  (no  neg.  valence),  sum  8. 

Abegg  *  suggested  that  the  sum  of  the  maximum  positive  and  negative 
valences  is  always  eight.  This  is  known  as  "  Abegg's  rule."  In  some 
cases  one  or  the  other  kind  is  more  or  less  latent.  For  example,  the 
halogens  are  more  commonly  negative  than  positive,  and  the  metals 
are  more  commonly  positive  than  negative.  In  cases  where  only  one 
kind  of  valence  is  known,  Abegg  regarded  the  other  as  completely  latent, 
as,  for  example,  in  sodium  or  calcium. 

Saturated  and  Unsaturated  Valence. — As  mentioned  above,  the 
organic  chemist  is  inclined  to  hold  that  the  carbon  atom  is  always 
tetravalent,  and  in  those  cases  where  the  structural  data  do  not  lend 
themselves  to  this  theory  he  resorts  to  the  use  of  some  rather  ingenious 
devices  to  account  for  the  facts.  The  cases  requiring  explanation  are 
those  in  which  the  atom  of  carbon  is  combined  with  too  few  elements 
or  groups  to  satisfy  its  four  valences.  The  organic  chemist  maintains 
that  in  such  cases  the  four  valences  exist  and  that  some  of  them  are 
"  unsaturated,"  or  "  self -saturated."  A  few  examples  will  show  what 
is  meant: 

Ethylene  gas  has  the  empirical  formula  C2H4.  If  we  write  this 
out  structurally  and  hold  to  the  idea  of  tetravalent  carbon,  we  obtain 
the  formula 

H    H 

.  ,       •      .   44- 

I  I 

H    H 

in  which  one  of  the  bonds  from  each  carbon  atom  is  unattached.  In 
the  same  way  the  carbon  atom  in  carbon  monoxide,  CO,  must  have 
two  free  bonds,  thus:  =C=O.  The  formula  for  acetylene  gas  is 
C2H2.  Structurally  this  becomes 

i    i 

H— C— C— H 

I      I 

In  this  case  each  carbon  atom  seems  to  have  two  free  bonds. 

*  Richard  Abegg  (1869-1909),  Professor  of  Chemistry,  University  of  Breslau. 


PRIMARY  AND  SECONDARY  VALENCE          79 

Instead  of  leaving  the  valence  bonds  free  as  shown  in  these  cases, 
it  is  customary  to  link  them  together,  forming  what  are  called  "  'double 
bonds  "  or  "  triple  bonds."  The  formulas  of  ethylene  and  acetylene 
would  then  become,  respectively, 

H    H 

and    H— C=C— H 
H 

The  ease  with  which  these  so-called  unsaturated  compounds  add  on 

uns  of  other  elements,  such  as  chlorine  and  hydrogen,  is  considered 
as  evidence  in  favor  of  the  theory  of  unsaturation.  Thus,  ethylene 
^easily  takes  on  hydrogen,  becoming  ethane,  C2He,  a  saturated  hydro- 
carbon. Oleic  acid,  an  unsaturated  acid  found  in  soft  fats  like  olive 
oil,  does  the  same  thing,  and  is  thus  changed  into  a  saturated  acid  called 
stearic,  forming,  at  the  same  time,  a  hard  fat  like  tallow. 

The  idea  of  unsaturation  carries  ^with  it  the  implication  that  an 
element  always  possesses  its  maximum  valence,  and  that  apparent 
lower  valences  are  cases  of  unsaturation.  Our  chapter  on  Atomic 
Structure  will  throw  light  on  this  subject  by  explaining  the  nature 
of  valence. 

Primary  and  Secondary  Valence. — Werner  *  has  made  a  most  care- 
ful study  of  many  complex  compounds  and  lias  come  to  the  conclusion 
that  valence  is  of  two  kinds.  Ordinary  valence,  such  as  we  have  been 
discussing,  he  calls  "  primary,"  and  the  other  type  he  calls  "  secondary." 
The  latter  is  defined  as  a  residual  attraction  left  over  after  the  primary 
valence  is  saturated. 

Werner's  theory  has  been  most  successful  as  applied  to  the  metal- 
ammonia  complexes,  but  he  makes  the  application  quite  general.  He 
recognizes,  among  these  compounds,  two  types  of  arrangement:  one 
in  which  four  radicals  or  elements  are  attached  to  a  central  atom  to 
form  a  non-ionizable  "  nucleus,"  and  a  second,  in  which  six  radicals  or 
elements  are  thus  attached.  Werner  speaks  of  these  numbers  as 
"  coordination  numbers."  Examples  of  the  two  types  are: 

Ck         .,NH3  Ck         ./NH3 

(A)          >Pt<"'  and        (B)     cACo:'  NH3 

CK       X-NH3  CK       \NH3 


*  "  New  Ideas  in  Inorganic  Chemistry"    [A.  Werner,  Professor  of  Chemistry, 
University  of  Zurich] . 


80 


CHEMICAL  VALENCE 


The  bonds  represent  primary  valence  and  the  dotted  lines  represent 
secondary  valence. 

Under  each  type  several  sub-types  may  exist.  Thus,  by  proper 
treatment  it  is  possible  to  replace  the  elements  attached  by  primary 
valence  with  radicals  attached  by  secondary  valence,  whereupon  the 
primary  valence  becomes  free  to  attach  elements  or  radicals  outside 
the  nucleus  and,  therefore,  ionizable.  In  type  A,  for  example,  the 
primary  chlorine  inside  the  nucleus  may  be  replaced  by  secondary 
NH3,  when  we  obtain 


C 


-NH3_ 


Cl 


"NH3 


or 


Cls 


the  chlorine  outside  the  nucleus  being  ionizable. 
These  formulas  may  be  written  more  simply  as 


Pt 


(NH3)j 


Ck 


Pt 


(NH3)3 
Cl 


Pt  (NH3)4 


Ck 


.  It  is  possible  also  to  replace  the  secondary  NH3  by  primary  acid  radical, 
when  the  nucleus  becomes  negative,  and  must  be  balanced  by  a  positive 
element  or  radical  outside,  thus: 


Pt 


(NH3) 


K,        and 


PtCU 


K2 


In  type  B  the  same  sort  of  substitution  may  also  be  made.  Begin- 
ning with  the  original  example  and  substituting  secondary  NH3  for 
primary  Cl,  we  obtain  such  compounds  as  the  following: 


(1) 


(2) 


Co 


Co 


(NH3)4 
Ck 


Cl 


(3) 


(4) 


Co 


(NH3)5 
Cl 


Co   (NH3)o 


Cl; 


C13 


or  by  substituting  primary  Cl  for  secondary  NH3  we  obtain  a  negative 
nucleus  able  to  attach  a  positive  ionizable  element  outside,  thus : 


(5) 


(NH3)2  "I 
Co  K 

CU 


(6) 


Co 


NH3 
Cls 


K2,    (7) 


CoCl6 


CHANGE  OF  VALENCE  81 

In  all  these  examples  under  type  B  the  cobalt  has  a  primary  valence 
of  three.  If  we  use  an  element  having  a  different  primary  valence  the 
coordination  number  remains  the  same,  but  the  number  of  ionizable 

I  radicals  changes.  This  is  obviously  necessary  when  we  remember 
that  the  ionizable  radicals  and  the  non-ionizable  of  the  same  kind 

-  are  both  attached  by  primary  valence.  If  we  use  a  central  element 
with  a  primary  valence  of  four  we  obtain  such  compounds  as 


(a) 


(NH3)2 
Pt 

C14 


This  compound  corresponds  to  (5)  above,  but  does  not  require  any 
positive  element  outside  the  nucleus,  because  the  primary  valence  of 
the  Pt  is  only  just  balanced  by  CU- 

(6)    [PtCl6]K2 

This  compound  corresponds  to  (7)  above,  but  requires  only  K2 
outside  the  nucleus  to  balance  the  two  extra  Cl  atoms  inside. 

In  KsFe(CN)6  the  central  element  is  iron,  with  a  primary  valence  of 
three.  The  coordination  number  is  6.  We  therefore  write: 

[Fe(CN)6]K3 

The  three  primary  valences  of  the  iron  are  balanced  by  3CN,  and 
the  extra  3CN  make  the  nucleus  trivalent  negative,  to  be  balanced  by 
Ka  outside.  This  corresponds  exactly  with  (7)  above. 

The  above  is  a  very  general  outline  of  Werner's  theory.  Although 
somewhat  vague  it  has  been  productive  of  a  vast  amount  of  splendid 
research,  and  for  that  reason  alone  has  been  very  valuable.  Many 
compounds  previously  unknown,  for  example,  have  been  predicted  and 
afterwards  produced,  while  the  effect  of  the  theory  on  the  study  of  va- 
lence has  been  valuable  although  not  final. 

Change  of  Valence  (Oxidation  and  Reduction). — The  term  oxidation 
originally  meant  the  addition  of  oxygen,  and  the  term  reduction,  the 
removal  of  oxygen.  We  still  use  these  terms  with  this  signification, 
but  their  meaning  has  now  been  extended  to  include  reactions  in  which 
oxygen  takes  no  part.  Oxidation,  as  we  shall  use  the  term,  means  an 

:  increase  of  positive  valence  (or  a  decrease  of  negative  valence) .     Reduc- 
tion is  the  reverse  of  this.     Thus,  ferrous  iron  is  oxidized  when  it  is 

!  changed  to  ferric,  for  the  bivalent  atom,  Fe++,  increases  in  positive 


82  CHEMICAL  VALENCE 

valence  and  becomes  a  trivalent  atom,  Fe+  ++.  Chlorine  radical  is 
oxidized  when  it  is  changed  to  chlorine  gas,  for  the  univalent  ion,  Cl~, 
increases  in  positive  valence  and  becomes  the  neutral  atom  Cl  (prefer- 
ably 2C1-— ^Ck).  Reduction,  in  both  these  cases,  would  mean  simply 
a  reversal  of  the  change  indicated,  Fe+  +  +  going  to  Fe++  and  Ck 
going  to  2C1~. 

An  oxidizing  agent  is  an  element  or  compound  which  has  the  power 
to  increase  the  positive  valence  of  some  other  element.  Probably  we 
may  as  well  say  that  an  oxidizing  agent  is  a  compound  or  an  element 
which  is  readily  reduced,  for  it  is  impossible  to  oxidize  one  thing 
without  at  the  same  time  reducing  another.  Chlorine  and  bromine 
are  good  oxidizing  agents,  and  when  they  thus  act  they  are  reduced 
to  Cl~  and  Br~,  respectively. 

A  good  reducing  agent  is  one  which  is  easily  oxidized.  Thus  stannous 
ion,  Sn++  is  a  good  reducing  agent  because  it  is  easily  changed  to 
stannic  ion,  Sn+  +  +  +  . 

When  an  oxidizing  agent  and  a  reducing  agent  react  upon  each 
other  the  total  change  in  valence  suffered  by  each  is  exactly  the  same, 
although  opposite  in  direction;  that  is,  the  total  positive  valence  lost 
by  the  oxidizing  agent  is  the  same  as  that  gained  by  the  reducing  agent. 
A  few  examples  will  make  this  clear: 

(1)  Fe+  +  +Br  ->  Fe+  +  +  -fBr~ 

The  reducing  agent,  Fe++,  has  gained  one  positive  valence,  becoming 
Fe+++,  and  the  oxidizing  agent,  Br,  has  lost  one  positive  valence, 
becoming  negative,  Br~. 

(2)  Sn+  +  +  2Cl  (or  C12)  -+Sn+  +  +  ++2Cl~ 

Bivalent  tin  has  become  tetravalent,  gaining  two  valences,  and  two 
atoms  of  neutral  chlorine  have  become  univalent  negative,  thereby 
giving  up  two  valences. 

(3)  SO2+O-»S03 

Tetravalent  sulphur  in  862  has  become  oxidized  to  hexavalent  in 
80s,  thus  gaining  two  valences.  Neutral  O  has  been  reduced  to  O~, 
thus  releasing  two  valences. 

(4)  When  zinc  acts  on  a  solution  of  some  copper  salt,  the  zinc  is 
oxidized   and  the  copper   is   reduced,    thus  Zn+Cu++ — >Cu+Zn++. 
The  zinc  gains  two  valences,  the  copper  gives  up  two. 


CHANGE  OF  VALENCE  83 

We  might  thus  continue,  but  we  should  never  find  an  exception: 
oxidation  and  reduction  are  mutual  and  exactly  identical  in  extent. 

We  often  have  occasion  to  speak  of  the  oxidizing  valence  or  the 
reducing  valence  of  an  element  or  compound,  and  by  this  we  mean, 
not  the  total  valence  possessed  by  the  atom  or  molecule,  but  the  change 
in  valence  suffered  when  the  substance  acts  in  this  capacity.  This  is 
very  important,  and  should  be  carefully  noted.  Thus  the  total  valence 
of  ferrous  iron,  Fe+  +  ,  is  two,  but  when  it  acts  as  a  reducer  its  change  of 
valence  is  one;  that  is,  it  changes  from  Fe++  to  Fe+  +  +  .  We  therefore 
say  that  ferrous  iron  is  a  univalent  reducing  agent. 

The  equivalent  weight  of  an  oxidizing  or  reducing  agent,  when  acting 
as  such,  is  understood  to  depend  on  its  oxidizing  or  reducing  valence, 
and  is  found  by  dividing  the  atomic  or  molecular  weight  of  the  agent 
by  this  valence.  The  matter  of  oxidizing  and  reducing  valence  and  the 
corresponding  equivalent  weights  is  so  important  that  we  shall  discuss 
several  common  cases  by  way  of  illustration.  The  secret  of  the  matter 
in  any  case  is  to  find  out,  first,  what  the  present  valence  is,  and  second, 
what  the  valence  becomes  when  the  agent  reacts.  The  difference  is  the 
valence  sought.  The  equivalent  may  then  be  determined  as  indicated 
above. 

(1)  Nitric  Acid.  —  Nitric  acid  may  be  prepared  by  treating  the 
oxide,  N20s,  with  water.  The  nitrogen  is  here  obviously  pentavalent 
positive,*  and  in  the  combination  with  water  no  change  of  valence 
occurs.  Nitrogen  in  nitric  acid  must,  therefore,  be  pentavalent  positive. 
This  is  shown  by  the  accepted  structural  formula 

HO—  N/ 


When  nitric  acid  acts  as  an  oxidizing  agent  it  changes  as  indicated  in 
the  equation 

2HNO3  ->  H2O+2NO+30t 

*  It  is  probably  safe  to  assume  that  oxygen  is  negative  in  any  ordinary  oxide, 

but  in  certain  cases  it  seems  to  be  positive.     Thus,  in  molecular  oxygen  one  atom 

+    _ 
may  be  positive  as  represented  in  the  formula  O+O—  ,  and  it  is  now  fairly  well  recog- 

nized by  organic  chemists  that  oxygen  may  function  as  tetravalent  positive  in  the 
so-called  "  oxonium  "  compounds.  Indeed,  liquid  water  (H2O)2  may  have  to  be 
represented  as  OH3OH,  "  oxonium  hydroxide,"  a  compound  analogous  to  ammonium 
hydroxide.  See  Collie,  Jour.  Ch.  Soc.,  75,  710,  and  many  later  references  in 
"  Abstracts  "  of  the  Am.  Chem.  Soc. 

t  It  may  also  change  under  certain  conditions  as  indicated  by  the  equation 

2HNO3  ->  H2O+2NO2+O 


84  CHEMICAL  VALENCE 

The  formula  NO  shows  that  the  nitrogen  has  become  bivalent  positive. 
One  molecule  of  nitric  acid  has  given  up  three  valences  to  something 
else  and  is,  therefore,  a  trivalent  oxidizing  agent.  Its  equivalent  weight 
as  an  oxidizing  agent  is  one-third  its  molecular  weight. 

When  nitric  acid,  a  trivalent  oxidizing  agent,  reacts  with  ferrous 
iron,  a  univalent  reducing  agent,  the  proportions  are,  obviously, 

HNO3  :  3Fe+  + 

(2)  Potassium  Permanganate.- — When  potassium  permanganate, 
KMnO4,  is  acted  upon  by  concentrated  sulphuric  acid  the  heptoxide 
of  manganese,  M^Oy,  is  produced.  The  valence  of  manganese  is  here 
evidently  seven  positive.  And,  since  the  sulphate  radical  from  the  acid 
is  neither  oxidized  nor  reduced,  we  infer  that  the  valence  of  the  man- 
ganese is  the  same  here  as  it  was  in  the  permanganate.  We  therefore 
write  the  structural  formula  for  KMn04  to  correspond,  thus; 

/O 

KO— Mn=O 
V) 

in  which  the  Mn  is  seen  to  be  heptavalent  positive. 

Potassium  permanganate  acts  as  an  oxidizing  agent  in  two  ways: 
(a)  In  neutral  or  alkaline  solution  it  changes  to  MnO2.  Here  the 
valence  of  the  manganese  is  seen  to  be  four  positive.  The  drop  in 
valence  for  one  molecule  of  KMnO4  in  neutral  solution  would,  therefore, 
be  from  seven  to  four,  or  three.  Potassium  permanganate  in  neutral  or 
alkaline  solution  is,  therefore,  a  trivalent  oxidizing  agent. 

(6)  In  acid  solution  potassium  permanganate,  acting  as  an  oxidiz- 
ing agent,  changes  to  Mn++  (as  seen,  for  example,  in  MnSO4).  The 
valence  of  the  manganese  is  here  two  positive.  The  drop  in  valence  for 
one  molecule  of  KMn04  in  acid  solution  is  from  seven  to  two,  that  is, 
five.  Potassium  permanganate  is  here,  therefore,  a  pentavalent  oxidiz- 
ing agent,  and  its  equivalent  weight  as  an  oxidizer  is  one-fifth  its  molecu- 
lar weight.  When  it  reacts  with  ferrous  iron  the  proportions  are 


KMnO4  :  5Fe++ 

(3)  Potassium  Bichromate. — Dichromic  acid,  H^C^Oj,  can  be  made 
from  chromic  anhydride,  CrOs,  by  addition  of  water.  The  valence  of  the 
chromium  is  six  positive  in  the  oxide,  so  we  infer  it  to  be  the  same  in  the 


CHANGE  OF  VALENCE  85 

acid,  or  in  its  salt,  K2Cr2O7.     Writing  the  structural  formula  to  corre- 
spond, we  have 

/5o 

KO— Crf 

>0 
KO— Cr< 


Each  chromium  atom  is  here  seen  to  be  hexavalent  positive;  and, 
since  there  are  two  of  these  atoms,  the  total  chromium  valence  in  the 
molecule  is  twelve.  When  the  dichromate  acts  as  an  oxidizing  agent 
the  chromium  changes  to  the  green  trivalent  form,  Cr+  +  +  .  The  drop 
in  valence  for  one  Cr  atom  is,  therefore,  three,  and  the  total  drop  for 
the  molecule  of  dichromate  is  evidently  six.  Potassium  dichromate  is, 
therefore,  a  hexavalent  oxidizing  agent,  and  its  equivalent  weight  is  one- 
sixth  its  molecular  weight. 

One  molecule  of  dichromate  reacts  with  six  atoms  of  ferrous  iron, 
thus: 

K2Cr2C7  :  6Fe++ 

(4)  Arsenious  Oxide. — The  arsenic  in  arsenious  oxide  is  trivalent 
positive.     This  oxide  is  a  reducing  agent,  and  in  acting  as  such  it 
changes  to  the  pentoxide,  As2Os,  in  which  the  arsenic  is  pentavalent 
positive.     The  change  of  valence  per  atom  of  arsenic  is  two,  but  the 
change  for  the  molecule  of  oxide  containing  two  atoms  is  four.     Arseni- 
ous oxide  is,  therefore,  a  tetravalent  reducing  agent. 

Arsenious  oxide  reacts  with  dichromate,  as  shown  by  the  ratio : 

2K2Cr2O7  :  3As2O3 

(5)  Hydrogen    Sulphide. — The    sulphur    in    hydrogen    sulphide    is 
bivalent  negative  as  represented  by  the  formula 


H 

The  compound  acts  as  a  reducing  agent,  and,  when  this  occurs,  the 
sulphide  ion  (S=)  becomes  oxidized  to  neutral  sulphur  (S),  and  is  pre- 
cipitated as  such.  The  change  of  valence  is  evidently  two,  making 
hydrogen  sulphide  a  bivalent  reducing  agent.  It  therefore  reacts  with 
dichromate  as  indicated  by  the  following  ratio : 

K2Cr2O7  :  3H2S 


86  CHEMICAL  VALENCE 

(6)  Sodium  Thiosulphate. — Thiosulphate  reacts  with  iodine  to  form 
the  tetrathionate,  Na2S4Oe.  The  equation  representing  the  change  may 
be  written: 

2Na2S2O3 +2I->Na2S4O6 +2NaI 

Thus,  two  molecules  of  thiosulphate  reduce  two  atoms  of  neutral  iodine 
to  I~~.     This  makes  the  salt  a  univalent  reducing  agent. 

Thiosulphate  is  used  only  with  iodine;  other  oxidizing  agents  destroy 
the  salt,  giving  free  sulphur  and  other  products. 


EXERCISES 

1.  Define  valence  in  terms  of  combining  capacity.     What  is  meant  by  "  uni- 
valent," "  bivalent,"  and  "  trivalent  "  elements?     Examples. 

2.  How  are  equivalent  and  atomic  weights  related  in  the  cases  of  univalent, 
bivalent,  and  trivalent  elements? 

3.  Cite  several  examples  showing  how  an  element  may  possess  variable  valence. 

4.  Show  how  fundamental  the  valence  of  an  element  is  in  determining  its  prop- 
erties. 

5.  In  what  way  is  a  so-called  "  structural  "  formula  superior  to  the   ordinary 
empirical  formula?     Examples. 

6.  Which  is  more  important  in  developing  a  structural  formula,  actual  structure, 
or  valence?     Discuss  several  examples. 

7.  What  is  meant  by  "  positive  "  and  "  negative  "  valence?     How  designated 
in  different  cases? 

8.  Write  and  discuss  structural  formulas  of  compounds  in  which  nitrogen,  chlo- 
rine, and  carbon  appear  with  positive  and  negative  valence.     Discuss  also  the  case 
of  the  elementary  gases. 

9.  Show  how  an  element  may  have  both  positive  and  negative  valence  at  once. 

10.  Discuss  Abegg's  rule,  with  examples. 

11.  Discuss  the  topic  "  saturated  and  unsaturated  valence." 

12.  What  two  kinds  of  valence  does  Werner  recognize? 

13.  Illustrate  Werner's  two  types  of  arrangement,  and  show  the  application  of 
his  two  kinds  of  valence. 

14.  Show  what  happens  when  primary  elements  inside  the  "  nucleus  "  are  replaced 
by  secondary  radicals,  or  when  secondary  are  replaced  by  primary.     (Illustrate  with 
type  A  complexes  and  show  how  the  coordination  number  and  valence  relations  are 
maintained  throughout.) 

15.  What  is  the  coordination  number  in  the  examples  of  cobalt  complexes  sub- 
mitted above?     Show  how  primary  and  secondary  substitution  i&  made  in  these 
cases  and  its  effect. 

16.  What  is  the  primary  valence  of  the  cobalt  in  the  cases  mentioned  in  15? 
Discuss  the  following  examples  with  reference  to  primary  valence,   coordination 
number,  sign  of  element  or  radical  outside  the  nucleus: 

r  (NHs)2i    r   i     r     i 

[Pt      Cl,  J,         [PtCI6jK2,         |Fe(CN)ejK3 


EXERCISES  87 

17.  What  is  meant  by  "  oxidation  "  and  "  reduction  "  as  referred  to  valence? 
Illustrate. 

18.  Define  oxidizing  and  reducing  agent,  and  illustrate. 

19.  Give  four  examples  showing  that  when  an  oxidizing  and  a  reducing  agent 
interact  the  change  in  valence  suffered  by  each  is  the  same,  though  opposite  in  sign. 

20.  What  is  meant  by  oxidizing  valence  or  reducing  valence?     Examples. 

21.  What  is  the  oxidizing  or  reducing  equivalent  of  an  element  or  compound. 

22.  Give  careful  discussion  of  the  oxidizing  or  reducing  valence  of  the  following 
compounds,  including  structure,  valence  of  principal  element,  nature    and  extent 
of  change,  manner  of  reacting : 

HNO3,  KMnO4,  K2Cr2O7,  As2O3,  H2S  and  Na2S2O3 

23.  What  volume  of  H2S  is  needed  to  reduce  10  gms.  of  FeCl3  to  FeCl2? 

24.  What  volume  of  chlorine  gas  (C12)  will  be  required  to  oxidize  the  FeCl2  in 
(23)  back  to  FeCl3? 

25.  What  weight  of  bromine  (Br2)  is  required  to  oxidize  8.5  gms.  of  H2S  to  free 
sulphur?     To  H2SO4? 

26.  How  many  cc.  of  a  molar  solution  of  nitric  acid  are  required  to  oxidize  10  gms. 
.of  FeSO4  to  Fe2(SO4)3  in  presence  of  H2SO4? 

27.  What  volume  of  M/10  KMn04  is  needed  to   oxidize  10  gms.  of  SnCl2  to 
SnCl4  in  presence  of  HC1? 

28.  What  weight  of  K2Cr2O7  is  needed  to  act  on  H2S  to  give  8  gms.  of  sulphur 
in  presence  of  H2SO4? 


CHAPTER  IX 
CLASSIFICATION  OF  THE  ELEMENTS:  THE  PERIODIC  SYSTEM 

Early  Attempts  at  Classification. — Probably  the  earliest  attempt  to 
point  out  any  fundamental  relationship  between  the  elements  was 
made  in  1815  by  the  English  physician,  Prout.  Partly  from  a  study 
of  his  own  work,  partly  from  that  of  others,  Prout  advanced  the  theory 
that  all  the  elements  were  made  up  of  hydrogen  atoms.  If  the  atomic 
weight  of  hydrogen  is  taken  as  1,  this  would  seem  to  require  that  all 
the  other  atomic  weights  should  be  whole  numbers.  Some  of  the 
atomic  weights  then  in  use  had  fractional  parts,  but  Prout  insisted 
that  these  were  due  to  errors  in  their  determination.  Berzelius,  of 
course,  could  not  accept  this,  for  many  of  his  values,  worked  out  with 
the  utmost  care,  were  not  whole  numbers.  However,  Dumas  and  his 
pupil,  Stas,  made  a  careful  redetermination  of  the  atomic  weights  of 
hydrogen  and  carbon,  and  did  find  them  to  be  exact  whole  numbers. 
This  caused  considerable  excitement  among  those  who  supported 
Prout,  and  encouraged  Stas,  who  was  one  of  these  supporters,  to  enter 
upon  his  wonderful  series  of  atomic  weight  determinations.  Stas  was 
soon  compelled  to  abandon  the  theory,  for  one  of  his  first  determinations 
was  that  of  chlorine,  which  he  found  to  be  35.45;  and  he  knew  that  it 
could  not  possibly  be  so  far  in  error  as  to  make  it  at  all  probable  that 
the  true  value  could  be  a  whole  number. 

After  Stas'  work,  Prout's  theory  was  for  a  time  considered  dead,  but 
since  then  it  has  reappeared  from  time  to  time  in  one  form  or  another, 
and  even  now  it  seems  to  be  the  sort  of  theory  that  people  would  like 
to  believe  in.  Quite  recently,  indeed,  Harkins  *  has  proposed  a  theory 
which  is  not  so  very  dissimilar,  namely,  that  the  elements  are  made 
up  of  hydrogen  and  helium  atoms.  This  theory  is  very  interesting  and 
plausible,  but  we  shall  leave  the  detailed  discussion  for  a  later  chapter 
where  it  more  properly  belongs. 

A  second  attempt  to  classify  the  elements  was  made  by  the  German 
chemist,  Doebereiner,  f  in  1817.  Doebereiner  noticed  that  the  elements 

*  Jour.  Am.  Chem.  Soc.,  37,  1367  and  1383. 

t  Johan  Wolfgang  Doebereiner  (1780-1849),  Professor  of  Chemistry  at  Jena. 
Noted  for  pioneer  work  on  catalysis. 


EARLY  ATTEMPTS  AT  CLASSIFICATION  89 

often  seemed  to  arrange  themselves  in  groups  of  three  (triads),  in 
which  the  elements  concerned  possessed  analogous  properties  and  a 
uniform  gradation  of  atomic  weights.  He  first  mentioned  the  group 
barium,  strontium,  and  calcium.  These  metals  are  called  the  "  alkaline 
earths,"  and,  as  everyone  knows,  are  much  alike  in  general  properties. 
The  atomic  weights  are:  Ba,  137;  Sr,  87.6;  and  Ca,  40.  The  mean  for 
Ba  and  Ca  is  88.5,  a  number  closely  approaching  the  value  for  Sr. 
Another  such  group  is  lithium,  sodium,  and  potassium,  three  strong 
alkalies.  The  atomic  weights  here  are:  Li,  6.9;  Na,  23;  and  K,  39.1 
The  mean  for  Li  and  K  is  exactly  23,  identical  with  the  value  for  sodium, 
the  middle  element  of  the  group.  Many  other  cases  of  good  agreement 
were  pointed  out.  In  one  case  the  middle  element  of  a  group  was 

lacking,  and  was  predicted.  This  was  the  group  chlorine, ,  and 

iodine.  The  atomic  weights  of  chlorine  and  iodine  were,  respectively, 
35.46  and  127.  The  atomic  weight  of  the  new  element  should  then 
be  the  mean,  81.23.  Bromine  was  discovered  about  this  time  and  was 
found  to  have  an  atomic  weight  of  80,  agreeing  very  well  with  the 
predicted  value. 

In  some  cases  the  agreement  was  not  so  good.  Take  the  analogous 
group,  fluorine,  chlorine,  and  bromine.  The  atomic  weights  are: 
F,  19;  Cl,  35.46;  Br,  80.  The  mean  for  F  and  Br  is  49.5,  not  at  all  in 
agreement  with  the  value  for  chlorine.  However,  even  the  discrepancies 
show  a  certain  kind  of  agreement  which  made  it  appear  likely  that  some 
fundamental  relationship  existed.  Nevertheless  it  scarcely  needs  to  be 
said  that  Berzelius  attacked  Doebereiner's  theory  as  he  had  Prout's. 
Indeed,  not  much  attention  was  paid  to  the  idea  at  all  until  about  1843, 
when  Gmelin,  also  a  German,  gave  it  an  extended  notice  in  his  textbook. 

A  still  later  attempt  at  classification  came  in  1865  when  Newlands,* 
an  English  chemist,  developed  what  he  called  the  "  law  of  octaves." 
He  found  that  if  he  arranged  the  elements  in  the  order  of  their  atomic 
weights  they  grouped  themselves  naturally  in  series  of  seven  (octaves), 
the  corresponding  elements  in  each  series  having  analogous  properties. 
The  following  is  an  adaptation  of  a  part  of  Newlands'  table: 

H  (1)          Li  (2)          Be  (3)  B  (4)  C   (5)         N  (6)          O  (7) 

F  (8)  Na  (9)        Mg  (10)      Al  (11)        Si  (12)        P  (13)         S  (14) 

Cl  (15)       K  (16)        Ca  (17)       Cr  (19)       Ti  (18)        Mn  (20)      Fe  (21) 

Although  Newlands'  attempt  was  very  imperfect,  it  will  be  noted 
that  each  time  we  pass  through  a  cycle  of  seven  elements  we  have  in 
general  a  return  of  analogous  properties.  Thus,  starting  with  lithium, 
we  pass  through  a  cycle  of  seven  and  come  to  sodium,  then  through 

*  John  A.  R.  Newlands  (1838-1898),  English  writer  on  Chemistry. 


90      CLASSIFICATION  OF  ELEMENTS:   THE  PERIODIC   SYSTEM 

another  cycle  of  seven  and  come  to  potassium,  all  elements  of  like 
properties.  The  same  thing  is  true  if  we  start  with  beryllium,  coming 
first  to  magnesium,  and  then  to  calcium.  It  is  true  that  there  are  some 
exceptions:  hydrogen,  for  example,  is  not  like  fluorine,  manganese  is 
not  like  phosphorus,  nor  is  iron  like  sulphur;  but,  on  the  whole,  New- 
lands'  arrangement  surely  shows  the  outlines  of  a  great  law.  Note 
the  fact  that  he  transposed  Cr  and  Ti  because  he  knew  titanium  must 
come  in  with  silicon.  As  we  know  now,  of  course,  he  should  have  left 
a  blank  space  where  he  places  Cr  (now  occupied  by  scandium),  and  Cr 
should  go  with  S  in  place  of  Fe. 

Newlands  gave  an  account  of  his  theory  to  the  Chemical  Society 
(London)  in  1866,  and  many  of  those  present  took  it  as  a  joke.  One 
member  sarcastically  inquired  whether  he  "  had  ever  examined  the 
elements  according  to  the  order  of  their  initial  letters."  When  he  sent 
in  his  paper  for  insertion  in  the  society's  journal  it  was  returned  to  him 
as  "  not  adapted  for  publication."*  Thus  it  goes  sometimes  with  a 
man  whose  ideas  are  in  advance  of  his  time. 

The  Modern  Periodic  Arrangement. — The  periodic  system  of  the 
elements,  in  nearly  its  present  form,  was  developed  independently  and 
nearly  simultaneously  by  the  Russian  chemist,  Mendeleeff,  f  and  the 
German  chemist,  Lothar  Meyer,  t  Meyer's  first  paper  appeared  in  his 
textbook  in  1864,  §  and  the  arrangement  proposed  was  similar  to 
that  of  Newlands.  Mendeleeff's  paper  appeared  in  1869. 1f  His 
system  was  also  based  on  that  of  Newlands,  or  at  least  contained  the 
same  germ  idea,  but  was  much  more  complete.  Meyer  afterwards 
changed  his  arrangement  to  that  of  a  continuous  spiral  or  helix.  This 
scheme  brought  out  very  clearly  the  continuous  nature  of  the  succession, 
and  was  just  as  successful  in  demonstrating  the  periodic  nature  of  the 
properties  of  the  elements.  Both  Meyer  and  Mendeleeff  left  blank 
spaces  into  which  none  of  the  known  elements  fitted,  and  predicted 
that  other  elements  would  be  discovered  to  fill  these  places.  In  several 
cases  these  predictions  have  been  realized. 

Since  the  time  of  Mendeleff  and  Meyer  the  system  they  developed 
has  been  considerably  expanded  by  the  addition  of  new  elements, 

*  Chem.  News.,  32,  22  (1875). 

t  Dmetri  I.  Mendeleeff  (1834-1907),  Professor  of  General  Chemistry,  University 
of  Petrograd.  See  Harrow,  Eminent  Chemist  of  Our  Time,  p.  19. 

J  Julius  Lothar  Meyer  (1830-1898),  Professor  of  Chemistry,  University  of 
Tubingen,  Germany. 

§  Die  modernen  Theorien  der  Chemie. 

1[Jour.  Russ.  Chem.  Soc.,  60  (1869).  See  also  "Faraday  Lecture"  delivered 
by  Mendeleeff  himself  twenty  years  later  (1889),  Jour.  Chem.  Soc.,  55,  634.  For  a 
splendid  sketch  of  Mendeleeff's  life  see  Harrow,  Eminent  Chemists  of  Our  Time,  p.  19. 


THE  MODERN  PERIODIC  ARRANGEMENT  91 

notably  the  group  of  inert  gases  from  the  atmosphere,  and  in  some 
other  ways  has  been  revised;  but  the  present  form  does  not  differ 
radically  from  theirs.  It  will  be  best  for  us  to  present  the  Periodic 
System  as  we  now  have  it,  and  then  proceed  to  a  discussion  of  the 
relationships  and  analogies  which  it  emphasizes.  In  the  table  on  page  92 
the  numbers  below  the  symbols  are  the  atomic  weights;  those  beside 
them  are  the  atomic  numbers,  that  is,  the  serial  numbers  of  the  elements. 

It  will  be  noted  at  once  that  the  elements  are  arranged  in  the  ascend- 
ing order  of  the  atomic  weights,  in  which  respect  the  arrangement  is 
like  Newlands'.  It  differs  from  his,  however,  in  beginning  with  helium 
instead  of  hydrogen.  Hydrogen  does  not  seem  to  fit  into  the  system 
at  all.  It  has  a  valence  of  one  which  should  place  it  in  Group  1,  but 
its  properties  certainly  do  not  ally  it  with  the  alkalies.  It  bears  the 
atomic  number  1  and  the  atomic  weight  1,  and  stands  just  outside  the 
system  as  a  sort  of  measuring  stick  for  the  comparison  of  other  elements. 

Beginning  with  helium,  we  pass  through  a  series  of  eight  elements 
ending  with  fluorine.  The  next  higher  element  in  atomic  weight  is 
neon,  another  inert  gas  very  much  like  helium.  It  is,  therefore,  placed 
under  helium,  and  thus  begins  the  second  period.  Again  we  pass 
through  a  series  of  eight,  when  we  come  to  chlorine.  Note  that  in 
every  case  the  elements  of  this  second  period  resemble  the  elements 
just  above.  Thus,  sodium  is  an  alkali  metal  like  lithium;  silicon  is 
like  carbon;  chlorine  is  like  fluorine.  Note  also  the  gradation  in 
properties:  We  start  with  a  perfectly  indifferent  substance,  helium: 
next  we  have  a  strong  alkali,  lithium;  then  we  have  a  weaker  alkali, 
beryllium;  following  this  is  boron,  which  is  almost  too  weak  a  base 
to  form  salts;  next  is  carbon,  which  acts  equally  well  as  acid  or  base; 
then  comes  nitrogen,  which  is  more  acidic  than  basic;  then  oxygen, 
still  more  acidic;  and  finally  fluorine,  the  most  acidic  of  all  the  ele- 
ments. If  we  were  to  turn  the  period  into  the  form  of  a  single  loop 
of  a  spiral,  we  should  have  helium,  the  inactive  element  on  one  side,  and 
carbon,  the  amphoteric  element,  on  the  other.  From  carbon  the 
properties  grade  on  one  side  towards  h'thium,  on  the  other  towards 
fluorine. 

The  second  period  shows  exactly  the  same  gradation  of  properties 
as  does  the  first. 

In  the  case  of  the  third  period  a  change  in  the  number  and  succession 
of  the  elements  will  be  noted.  Beginning  with  argon  and  passing 
through  a  series  of  eight,  we  do  not  then  come  to  another  of  the  inert 
gases;  instead  we  pass  through  a  series  of  the  three  elements,  iron, 
nickel,  and  cobalt,  which  form  a  transition  between  manganese  on 
the  one  hand  and  copper  on  the  other.  Continuing  beyond  copper  we 


92        CLASSIFICATION  OF  ELEMENTS:  THE  PERIODIC  SYSTEM 


8? 

2s 


££ 


9  1* 

21 


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OS 


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ll 


co«o 
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THE  MODERN  PERIODIC  ARRANGEMENT  .93 

pass  through  another  series,  and  finally  end  with  bromine.  This  period, 
containing  two  series  and  the  transition  group,  is  called  a  "  double  " 
or  "  long  "  period.  Note,  now,  the  correspondence  in  properties.  At 
the  beginning  the  correspondence  is  perfect;  argon  is  like  neon,  and 
potassium  is  like  sodium.  As  we  proceed,  however,  the  correspondence 
gradually  fails,  the  elements  remaining  too  basic.  Manganese,  for 
example,  is  very  little  like  chlorine.  As  we  proceed  with  the  second 
series,  however,  the  correspondence  reappears;  and  by  the  time  we 
reach  bromine  is  perfect  again.  The  placing  of  the  symbols  in  the 
table  to  the  right  or  left  side  of  the  spaces  they  occupy  brings  out  the 
degree  of  correspondence,  those  showing  the  greatest  similarity  standing 
in  the  same  vertical  line. 

The  fourth  and  fifth  periods  are  also  double,  containing  two  series 
each  with  a  transition  group  between.  Between  cerium  and  tantalum 
'  in  the  fifth  period  we  find  a  leap  of  over  forty  units  in  the  atomic  weights, 
although  tantalum  certainly  belongs  in  the  same  group  as  columbium. 
It  is  here  in  this  gap  that  the  anomaly  of  the  rare  earth  elements  occurs. 
The  atomic  weights  and  the  atomic  numbers  of  these  elements  place 
them  here,  but  their  properties  absolutely  exclude  them.  What  to  do 
with  them  has  not  been  satisfactorily  settled. 

The  sixth  period  is  incomplete;  but,  as  far  as  known,  the  elements 
belong  to  the  so-called  radioactive  type.  It  seems  to  be  the  beginning 
of  a  double  period,  for  the  correspondence  between  the  latter  members 
and  those  above  them  is  not  good.  However,  we  have  no  evidence  of 
any  element  of  higher  atomic  weight  than  uranium. 

There  are  four  gaps  in  the  system,  belonging  to  undiscovered  ele- 
ments. Their  atomic  numbers  are  43,  75,  85,  and  87. 

Note  that  the  increment  in  the  atomic  weights  from  left  to  right 
is  something  over  2,  making  the  atomic  weight  of  an  element  always  a 
little  more  than  twice  the  atomic  number. 

There  is  one  other  matter  of  general  importance:  at  three  places  in 
the  table  it  has  been  necessary  to  transpose  the  order  called  for  by 
the  atomic  weights.*  Thus  argon  has  a  higher  atomic  weight  than 
potassium,  cobalt  than  nickel,  and  tellurium  than  iodine.  Placing 
these  elements  in  the  order  called  for  by  the  atomic  weights  would  be 
„  obviously  absurd,  however,  for  that  would  place  the  inert  gas,  argon, 
with  the  alkali  metals,  and  would  remove  iodine  from  the  other  halogens. 
The  atomic  number,  however,  does  not  show  this  anomaly,  and  for  this 

*  These  transpositions  have  called  out  some  splendid  research  calculated  to  deter- 
mine whether  the  atomic  weights  in  these  cases  are  correct.  See,  for  example, 
Brouner,  Jour.  Chem.  Soc.,  55,  382,  Experimental  Researches  on  the  Periodic  Law: 
Tellurium. 


94      CLASSIFICATION  OF  ELEMENTS:  THE  PERIODIC  SYSTEM 


reason  we  are  inclined  to  say  that  the  properties  of  the  elements  depend 
more  fundamentally  on  atomic  number  than  on  atomic  weight. 

We  shall  now  proceed  to  take  up  in  detail,  first,  the  relations  seen 
in  passing  through  the  periods  from  left  to  right  (periodic  functions) 
and,  second,  the  relations  seen  in  passing  down  through  the  groups. 

Periodic  Functions. — The  most  fundamental  principle  of  the  Periodic 
System  is  the  fact  that  the  properties  of  the  elements,  both  physical 
and  chemical,  are  periodic  functions  of  the  atomic  weights  (and  of  the 
atomic  numbers).  We  shall  point  out  this  relationship  in  the  case  of 
several  important  properties : 

(1)  Valence. — The  valences  most  characteristic  of  each  group  of 
elements  are  indicated  at  the  top  of  the  table.  Thus  the  elements  of 
the  O  group  form  no  compounds  and,  therefore,  have  no  valence. 
This  is  indicated  by  use  of  the  symbol  R,  referring  to  the  element. 
It  will  be  noted  that  the  fundamental  positive  valence  is  in  each  case 
the  same  as  the  number  of  the  group.  In  group  1  it  is  1,  in  group  2 
it  is  2,  etc.,  up  to  group  8,  where  the  positive  valence  is  8.  These 
positive  valences  are  indicated  by  the  general  formulas  of  the  oxygen 
compounds,  thus:  R2O,  RO,  etc.  Beginning  with  group  4  the  elements 
show  a  negative  valence.  In  group  4  this  is  the  same  as  the  positive 
valence,  but  from  there  on  it  decreases  regularly  to  group  8,  where  it 
becomes  0.  The  negative  valence  is  indicated  by  general  formulas 
of  hydrogen  compounds,  thus:  RH4,  RHs,  etc.  If  we  accept  Abegg's 
theory  that  a  latent  negative  valence  exists  in  those  cases  where  no 
corresponding  compounds  occur,  we  note  a  very  interesting  relationship, 
thus : 


t\. 

cu 

C\o. 

M> 

tfOv 

<fc>v 

Group 

0 

1 

2 

3 

4 

5 

6 

7 

8 

-(-valence 

+0 

-fl 

+2 

+3 

+4 

+5 

+6 

+7 

+8 

—valence  

(-8) 

(-7) 

(-6) 

(-5) 

-4 

-3 

-2 

-1 

-0 

It  will  be  instructive  also  to  present  a  list  of  typical  compounds, 
showing  the  periodic  gradation  of  positive  and  negative  valence: 

It  will,  doubtless,  be  remembered  that  many  of  the  elements  have 
other  valences  than  those  characteristic  of  the  group.  Thus,  copper  is 
usually  bivalent  instead  of  univalent,  while  manganese  shows  the 
valences  2,  3,  4,  and  6  as  well  as  7,  and  of  these,  2  is  perhaps  the  com- 
monest* We  shall  refer  to  this  matter  again  under  the  group 
discussions. 


PERIODIC  FUNCTIONS 


95 


Group 

0 

1 

2 

3 

4 

5 

6 

7 

8 

Li2O 

BeO 

B203 

C02 

N205 

SO3 

HClOt 

OsO4 

LiCl 

BeCl2 

BCla 

ecu 

P.05 

CrO3 

HBrO4 

RuO4 

NaCl 

MgO 

A1203 

SiO2 

PC15 

Se03 

Mn2O7 

Pos 

K2O 

MgCl2 

A1C13 

SiCl4 

As2O5 

MoO8 

HMnO4 

.ros  < 

KC1 

CaO 

ScCl3 

SnO2 

TaBr5 

TeO3 

HIO4 

AgCl 

CaCl2 

La2O3 

SnCl4 

WO3 

Ag20 

SrCl2 

T12O3 

PbO2 

WC16 

Au2O 

BaCl2 

T1C1, 

ThO2 

CH4 

NH3 

H2O 

HC1 

SiH, 

PH3 

H2S 

HBr 

Nee.  . 

AsH3 

H2Se 

HI 

SbH3 

H2Te' 

(2)  Add-  and  Base-forming  Nature. — We  have  already  shown  in 
the  general  discussion  how  the  periods  start  with  a  strongly  basic 
element  and  end  with  one  which  is  strongly  acidic,  the  first  period,  for 
example,  beginning  with  lithium  and  ending  with  fluorine.  The  first 
group  is  called  the  alkali  group.  All  the  characteristic  elements  of  this 
group  form  strong  bases,  like  NaOH,  which  turn  litmus  blue  and  have  a 
strong  soapy  feel.  The  hydroxides  of  group  2  are  also  alkaline,  but 
are  considerably  weaker  than  those  of  group  1.  They  are  called  the 
alkaline  earths.  Characteristic  compounds  are  Mg(OH)2  and  Ca(OH)2, 
both  of  which  are  rather  caustic.  In  the  third  group  the  basic  nature 
becomes  weak  and  the  acidic  nature  begins  to  appear.  Thus,  Al(OH)s 
acts  as  a  base,  dissolving  in,  say,  HC1  to  form  Aids,  or  in  NaOH  to  form 
NasAlOs.  It  is  more  characteristically  basic  than  acidic,  however, 
as  we  should  expect  of  this  group  which  lies  nearer  the  basic  side  of  the 
system.  The  fourth  group  is  the  typically  amphoteric  group,  producing 
acids  and  bases  of  about  equal  strength.  Carbon  forms  CCU  *'  and 
H2CO3;  tin  forms  SnCU  and  H2SnO3.  In  group  5,  the  acidic  property 
predominates.  Thus  we  have  HNOs,  a  strong  acid,  also  HPOs  and 
HsP04,  moderately  strong  acids.  Nitrogen  and  phosphorus  form  no 
true  salts  at  all.  It  is  true  that  such  a  compound  as  PCls  exists,  but  it 
is  instantly  decomposed  by  water,  indicating  the  extremely  weak 
basic  nature  of  the  element.  The  elements  of  group  6  are  almost 
entirely  acidic.  Oxygen,  for  example,  never  forms  a  salt  by  replacing 
the  hydrogen  of  an  acid.  There  are,  however,  some  elements  in  the 
group  which  have  a  rather  latent  basic  nature.  Thus  we  have  WCle. 

*  Carbon  tetrachloride  is  a  liquid  which  can  hardly  be  classed  as  a  salt,  although 
the  formula  so  appears. 


96      CLASSIFICATION  OF  ELEMENTS:  THE  PERIODIC  SYSTEM 

In  group  7  we  have  no  basic  properties  at  all,  except  in  the  case  of 
manganese,  an  element  which  belongs  to  the  first  series  of  a  double 
period,  and  shows  practically  no  group  correspondence. 

(3)  Atomic  Volume. — Atomic  volume  is  the  volume  occupied  by  a 
gram-atomic  weight  of  substance,  and  is  found  by  dividing  the  gram- 
atomic  weight  by  the  density.  Thus  the  gram-atomic  weight  of  sodium 
is  23  gms.  and  the  density  is  0.97.  The  atomic  volume  is  23/0.97,  or 
23.7  cc. 

If  we  work  out  the  atomic  volumes  of  all  the  elements  in  this  way, 
and  then  plot  them  against  the  atomic  weights,  we  obtain  the  very 


20   40 


100   120   140   160 
Atomic  Weights 


180   200   220   240 


FIG.  5. — Graph  of  Atomic  Volumes.* 


instructive  graph  shown  above.  No  graph  could  bring  out  more 
clearly  than  this  one  the  wonderful  interrelationship  of  the  elements. 
Let  us  note  a  few  instances :  In  the  first  place  note  the  splendid  periodic 
nature  of  the  function,  each  group  forming  a  great  U-shaped  curve. 
Note  also  the  fine  way  in  which  the  long  periods  are  emphasized,  with 
no  indication  of  a  double  series  arrangement.  The  alkali  metals  have 
the  highest  atomic  volumes  and,  therefore,  stand  at  the  peaks  of  the 


Fourteen  rare  earth  metals  come  between  cerium  and  tantalum. 


PERIODIC  FUNCTIONS  97 

curves.  The  probability  that  another  alkali  metal  is  yet  to  be  dis- 
covered is  well  shown  also.  All  the  inert  gases  appear  on  the  left  sides 
of  the  peaks,  with  the  halogens  just  below  them.  Another  halogen 
remains  to  be  discovered.  The  alkaline  earth  metals  come  to  the  right 
of  each  peak,  radium  taking  its  proper  place  with  the  others.  The  three 
transition  groups  all  come  at  the  lowest  points  of  the  double  period 
curves,  these  having  very  small  atomic  volumes.  Finally,  our  coin 
metals — copper,  silver,  and  gold — all  come  just  around  the  turn  of  the 
large  curves  next  to  the  transition  groups. 

Relations  Inside  the  Groups. — In  passing  down  through  the  groups 
from  period  1  to  period  6,  the  changes,  although  not  so  radical,  are  just 
as  important  as  those  seen  in  passing  through  the  periods. 

The  Zero  Group. — There  are  six  of  the  inert  gases,  including  niton, 
or  "  radium  emanation."  The  atomic  weights  range  from  4  for  He  to 
222.4  for  Nt.  They  form  no  compounds,  of  course,  and  therefore  cannot 
be  compared  with  respect  to  any  chemical  activity.  They  do  show  a 
gradation,  however,  in  physical  properties  with  increasing  atomic 
weight.  Thus,  helium,  the  lowest  in  atomic  weight,  has  the  lowest 
density  and  the  lowest  atomic  volume,  and  is  the  hardest  to  liquefy. 
Helium  has  the  lowest  atomic  weight  of  any  element  in  the  periodic 
system  and  has  the  least  activity;  in  other  words,  it  is  the  most  inert 
substance  in  existence. 

The  story*  of  the  discovery  of  these  rare  gases  reads  like  a 
romance  and  serves  to  bring  out  in  a  splendid  way  the  great  practical 
value  that  may  often  arise  when  some  strange,  abnormal  behavior 
is  carefully  followed  up  just  for  the  sake  of  scientific  accuracy  and 
completeness. 

Group  1. — The  first  two  members  of  this  group — lithium  and  sodium 
— "  set  the  pace,"  so  to  speak,  for  the  rest  of  the  group.  These  two 
elements  represent  the  two  short  periods.  Below  these  we  note  two 
distinct  kinds  of  elements,  potassium,  rubidium,  and  caesium  on  the  one 
hand,  and  copper,  silver,  and  gold  on  the  other.  The  first  three  corre- 
spond perfectly  with  the  type  members  of  the  group,  and  so  may  be 
considered  the  characteristic  members.  The  others  stand  by  them- 
selves, quite  closely  interrelated  but  showing  very  little  likeness  to  the 
characteristic  members.  Note  that  the  characteristic  elements,  the 
alkalies,  stand  at  the  head  of  the  first  series  of  a  double  period,  while 
the  corresponding  heavy  metals  stand  at  the  head  of  the  second  series 
in  the  same  periods.  The  following  table  of  properties  will  help  to  bring 
out  some  of  the  likenesses  and  contrasts : 

*  A  fine  summary  of  this  story  may  be  found  in  McCoy  and  Terry's  "  Intro- 
duction to  General  Chemistry,"  pp.  507-513.  It  should  be  read  by  everyone. 


98      CLASSIFICATION  OF  ELEMENTS:  THE  PERIODIC   SYSTEM 


Li 

Na 

K 

Ru 

Cs 

Cu 

Ag 

Au 

Atomic  weight  .  .  . 
Density  .  . 

6.94 
0.53 
11.9 

186° 
1400° 

form  b 
hig 

23.0 
0.97 
23.7 
97° 
750° 
un 
all 
a,ses,  Li  \ 
h,  ascem 
alwaj 

39.1 
0.87 
44.8 
62° 
712° 
iformly 
very  so 
veakest 
ling  ore 
rs  comb 

85.45 
1.52 
56.1 
38.5° 
696° 
1 
ft 
Cs  str< 
er  Li—  > 
ined 

132.8 

1.87 
70.6 
26.4° 
670° 

Dngest 
Cs 

63.6 
8.93 
7.1 
1083° 
2310° 
2orl 
moc 

low,  c 
gei 

107.88 
10.5 
10.2 
961° 
1955° 
1 
erately  1: 
no  actio 
>rder  Au- 
icrally  fr 

197.2 
19.3 
10.2 
1063° 
2500° 
3orl 
lard 
n 
->Cu 
ee 

Atomic  volume  .  . 
Melting  point  .... 
Boiling  point  
Valence  
Hardness  

Action  on  water  .  . 
Displacing  power  . 
Occurrence  

The  likeness  and  regularity  of  conduct  among  the  members  of  either 
sub-group  are  obvious:  Note  how  the  properties  of  the  alkalies  either 
follow  with  the  ascending  order  of  the  atomic  weights  or  take  on  a  reverse 
order.  Note  the  uniformity  of  valence  (1),  the  softness,  their  great 
reactivity  coupled  with  the  dependent  fact  that  they  always  occur 
combined,  also  the  fact  that  they  all  form  strong  soluble  bases.  Note 
particularly  also  that  the  bases  formed  grade  up  decidedly  in  strength 
from  LiOH  to  CsOH.  The  latter  is  the  strongest  base  known.  The 
violence  of  the  reaction  with  water  is  in  the  same  order :  lithium  reacts 
moderately,  never  taking  fire;  caesium  reacts  with  explosive  violence. 
The  reaction  with  water  indicates  also  the  order  of  displacement: 
caesium  will  be  found  at  the  very  top  of  the  displacement  (electromotive) 
series,  and  is  thus  branded  as  the  most  active  of  the  positive  elements. 

Among  the  members  of  the  other  sub-group  the  regularities  are  not 
so  marked,  but  likenesses  are  not  lacking.  Thus,  these  metals  all  melt 
near  1000°.  They  all  have  very  low  atomic  volumes.  They  are  of 
about  the  same  hardness  and  are  very  malleable  and  ductile.  They 
do  not  react  with  water,  and  their  general  reactivity  is  very 
low,  placing  them  at  the  very  bottom  of  the  electromotive  series.  In 
this  connection  it  is  important  to  note  also  that  the  order  of  displacement 
is  the  reverse  of  that  found  among  the  alkalies,  gold  having  the  least, 
and  copper  the  greatest,  displacing  power.  On  account  of  their  slight 
reactivity,  they  all  occur  in  the  free  condition.  Finally,  they  are  the 
three  best  conductors  of  heat  and  electricity. 

The  contrasts  between  the  two  sub-groups  are  obvious.  We  need 
not  mention  them  again,  since  the  above  discussion  has  already  empha- 
sized them. 

The  general  arrangement  of  this  group  is  typical :  two  type  elements 
at  the  top;  two  sub-groups  below,  one  generally  showing  better  corre- 


RELATIONS  INSIDE  THE  GROUPS 


99 


spondence  with  the  type  members  than  the  other;  and,  most  important 
of  all,  the  fine  family  relationships.  The  left-hand  sub-group  is  usually 
designated  as  the  A  sub-group  and  the  right-hand  one  as  the  B  sub- 
group. We  shall  so  designate  them  from  now  on. 

Group  2. — The  first  two  members  of  this  group  are  beryllium  and 
magnesium.  These  are  typical.  They  form  bases,  which,  however, 
are  not  so  strongly  alkaline  nor  so  soluble  as  the  true  alkalies.*  They 
are  bivalent. 

Below  these  typical  elements  come  the  other  alkaline  earth  metals : 
calcium,  strontium,  barium,  and  radium  on  the  one  hand,  and  the  heavy 
metals,  zinc,  cadmium,  and  mercury  on  the  other.  The  best  corre- 
spondence comes,  of  course,  in  the  case  of  the  alkaline  earths  (sub- 
group A).  The  correspondence  on  the  other  side  is  not  so  poor,  how- 
ever, as  in  group  1  B.  Metallic  zinc,  for  example,  is  not  so  unlike 
magnesium,  and  both  metals  form  white  oxides  and  hydroxides,  the 
latter  being  in  both  cases  nearly  insoluble  in  water. 

A  table  of  properties  will  be  enlightening,  as  in  group  1 : 


Be 

Mg 

Ca 

Sr 

Ba 

Ra 

Zn 

Cd 

Hg 

Atomic  weight  .  .  . 
Density  
Atomic   volume  .  . 
Melting  point.  .  .  . 
Valence        .... 

9.1 
1.85 
5 
960° 
2 

43 

24.3 
1.74 
14 
651° 
2 

O21 

26 
al 
all 
rat! 

40 
1.54 
26 
850° 

2 

0.17 

0.20 
moder 
but  Be 
ler  high 

87.6 
2.54 
34 
900° 

2 

0.68 

0.01 
ately  sc 
form  bg 
,  order 

137.3 

3.80 
35 
850° 

2 

3.9 

0,1 

ft 
tses 
Be->E 

226 
2 

A 

65.3 
7.1 
9 
419° 
2 

034 

57 
ra 
n 
low,  c 

112.4 
8.6 
13 
321° 

2 

032 

76 
ther  hai 
o  actioi 
rder  Hj 

200.6 
13.6 
14.5 
-39° 
2  or  1 

025 

rd 
l 

?-»Zn 

Solubility  of 
Hydroxide  l.  .  .  . 
Solubility  of 
Sulphate1  
Hardness.  .      .    . 

Action  on  water  .  . 
Displacing  power  . 

1  In  gm.  per  100  cc.  water  at  20°  C.     The  inferior  figures  indicate  number  of  zeros,  thus  Os 
means  .000. 

We  note  here  somewhat  the  same  family  relationships  and  gradations 
as  in  group  1.  In  sub-group  A  we  may  mention  the  increase  of  atomic 
volume  with  increasing  atomic  weight;  the  uniform  valence  of  2;  the 
opposite  gradation  in  the  solubility  of  the  hydroxide  and  sulphate ;  and, 
above  all,  the  increase  in  activity  from  Be  to  Ra.  Beryllium  does  not 
react  with  water  even  at  100°  and  its  base,  Be(OH)2,  is  more  like  that 

*  Be  (OH)  2  is  amphoteric  and  scarely  basic  at  all. 


100    CLASSIFICATION  OF  ELEMENTS:  THE  PERIODIC  SYSTEM 

of  aluminum  than  those  of  the  other  alkaline  earths.  In  sub-group  B 
we  note  rather  similar  properties;  but  density  is  much  higher,  mercury 
has  two  valences,  and  these  metals  do  not  react  with  water.  Also,  the 
order  of  displacement  is  the  reverse  of  that  seen  in  sub-group  A,  as  in 
group  1. 

Group  3. — This  group  starts  off  with  boron  and  aluminum.  Of 
these,  aluminum  is  much  more  characteristic  of  the  group.  Boron  is 
more  like  silicon,  the  second  member  of  group  4,  just  as  beryllium  in 
group  2  was  like  aluminum  in  group  3.  Boron  is  more  acidic  than 
basic,  although  it  does  form  such  salts  as  BFs  and  BCls.  Its  hydroxide 
acts  only  as  an  acid  (boric  acid) .  Aluminum  is  truly  amphoteric,  form- 
ing a  hydroxide,  Al(OH)s,  which  dissolves  in  acids  to  form  aluminum 
salts  (e.g.,  Aids)  and  in  bases  to  form  aluminates  (e.g.,  NaAlO2). 

Below  aluminum,  the  group  divides  as  do  groups  1  and  2.  Sub- 
group A  includes  scandium,  yttrium,  lanthanum,  and  actinium;  sub- 
group B  includes  gallium,  indium,  and  thallium.  So  far  as  charac- 
teristic properties  go  we  find  it  hard  to  decide  which  sub-group  shows 
the  better  correspondence,  but  we  shall  probably  still  have  to  choose  A 
instead  of  B,  for  some  of  the  members  of  sub-group  B  are  amphoteric 
while  those  of  A  are  not.  We  have  somewhat  the  same  gradation  of 
basicity,  however,  as  in  the  previous  groups.  Thus,  while  aluminum 
hydroxide  is  very  weak,  lanthanum  hydroxide,  La(OH)3,  is  a 
rather  strong  base,  giving  an  alkaline  reaction  with  litmus,  for 
example.  On  the  other  hand,  while  gallium  and  indium  are  amphoteric, 
thallium  is  not.  Thallium  forms  two  hydroxides;  thallous  hydroxide, 
T1OH,  which  is  a  very  soluble,  strong  base,  and  thallic  hydroxide, 
T1(OH)3,  a  weak  insoluble  base.  It  is  worth  repeating  in  this  connection 
what  we  have  said  before — namely,  that  valence  is  a  very  fundamental 
property.  Thallium  with  a  valence  of  one  is  quite  a  different  element 
from  thallium  with  a  valence  of  three.  Univalent  thallium  acts  more 
like  the  alkali  metals  than  like  a  typical  third-group  element.  We  have 
just  such  a  fundamental  difference  also  in  the  case  of  univalent  copper 
and  mercury.  In  making  group  comparisons  we  must  always  be  careful 
to  take  an  element  with  the  characteristic  group  valence. 

The  "  rare  earth  elements,"  mentioned  before,  seem  to  belong  in  the 
third  group  when  their  properties  are  considered,  but  their  atomic 
weights  place  them  between  the  fourth  and  fifth  groups.  Just  how  they 
can  be  included  in  the  system  is  an  unsolved  problem. 

Group  4. — Carbon  and  silicon  stand  at  the  head  of  this  group. 
They  are  typically  amphoteric.  Below  these  we  find  on  the  A  side 
titanium,  zirconium,  cerium,  and  thorium,  and  on  the  B  side  germanium, 
tin,  and  lead.  Both  groups  are  more  or  less  amphoteric. 


RELATIONS  INSIDE  faa&fctttKJPS1'*"*  ***•  *'**•    101 


'We  must  not  forget  that  it  is  in  this  group  that  negative  valence 
first  appears.*  Carbon  and  silicon  are  the  only  elements  of  the  group 
to  show  it,  however:  note,  for  example,  the  compounds  CELi  and  SiH4. 

Several  of  the  elements  of  this  group  also  show  positive  valences 
lower  than  the  group  number,  which  is  four.  Thus,  carbon  forms  CO, 
lead  forms  PbO  and  other  compounds  in  which  lead  is  bivalent.  Tin 
is  bivalent  in  stannous  compounds,  and  cerium  is  trivalent  in  its  more 
stable  salts,  like  cerous  nitrate,  Ce(N03)3- 

Group  5.  —  The  leaders  in  this  group  are  nitrogen  and  phosphorus, 
typical  pentavalent  elements  almost  entirely  acid-forming  in  their 
nature. 

Below  these,  sub-group  A  includes  vanadium,  columbium,  tantalum, 
and  the  radioactive  element,  uranium  —  X2,  while  sub-group  B  includes 
arsenic,  antimony,  and  bismuth.  The  correspondence  is  undoubtedly 
now  on  the  B  side,  for  arsenic  is  very  like  phosphorus,  although  there  is 
little  to  choose  between  tantalum  and  bismuth. 

Negative  valence  appears  with  four  members  of  this  group  in  the 
compounds  'NHs,  PHs,  AsHs,  and  SbHs.  Of  these,  NHs  alone  forms 
with  water  a  basic  hydroxide  (NH4OH),  although  phosphorus  forms  an 
analogous  chloride,  PH4C1,  called  phosphonium  chloride. 

Group  6.  —  The  characteristic  valence  of  this  group  is  six,  but  oxygen, 
the  first  member,  does  not  show  it.  Sulphur,  the  second  member,  with 
its  oxygen  compound,  SOs,  is  more  typical.  Below  this  we  find,  in 
the  A  line  of  succession,  the  elements  chromium,  molybdenum,  tungsten, 
and  uranium;  on  the  B  side,  selenium,  tellurium,  and  polonium.  Since 
selenium  and  tellurium  are  the  exact  analogues  of  sulphur,  we  have  on 
this  side  the  true  group  correspondence. 

Typical  compounds  of  this  group  are  K^SO^  K^CrO^  K^SeO^  and 
K2Te04,  in  all  of  which  the  central  element  has  a  valence  of  +6.  Other 
positive  valences  are  shown  in  such  cases  as  SO2,  CrCls,  CrCl2,  etc.,  in 
which  the  elements  concerned  do  not  exhibit  the  true  group  relationship. 

The  elements  of  sub-group  A  are  considerably  more  metallic  than  the 
others.  Thus,  we  have  chromium  and  molybdenum  alloying  with  iron 
to  form  special  tool  steels,  and  tungsten,  the  metal  which  furnishes  us 
the  filaments  in  our  electric  lamps. 

Negative  valence  is  shown  by  four  members  in  the  compounds 
H20,  EkS,  EkSe,  and  H^Te.  Of  these,  water  is  the  most  stable  at  high 
temperatures,  and  hydrogen  telluride  the  least  stable. 

It  is  rather  interesting  that  while  the  hydroxide  of  sulphur,  SO2(OH)2 
(more  commonly  written  H2SO4),  is  a  strong  acid,  the  analogous  hydrox- 

*  Unless  in  the  alkali  hydrides,  like  NaH,  the  metals  possess  negative  valence. 


102    OLAS&YFICATm*N:OF;ELEMENTS:  THE  PERIODIC  SYSTEM 

ide  of  uranium,  U02(OH)2,  is  a  basic  substance.  All  the  common  salts 
of  uranium  may  be  considered  as  derived  from  this  base.  Thus  we  have 
U02(N03)2,  UO2SO4,  etc.  The  group  UO2  is  called  "  uranyl." 

Group  7. — In  group  7  we  have  the  most  highly  acidic  of  the  elements. 
Of  these,  fluorine  stands  at  the  head,  not  only  in  its  position  in  the  group, 
but  also  in  its  activity.  Caesium,  placed  at  the  bottom  of  group  1,  was 
the  most  active  positive  element;  and  fluorine,  placed  at  the  top  of 
group  7,  is  the  most  active  negative  element.  Note  the  relative  position 
of  these  two  elements  in  the  system  as  a  whole. 

Chlorine  is  the  second  member  of  the  group,  and  below  this  come 
the  two  sub-groups.  A  contains  only  one  element,  manganese,  while 
B  contains  the  other  halogens,  bromine  and  iodine.  There  is  no  ques- 
tion, of  course,  as  to  which  sub-group  shows  the  correspondence  here, 
for  manganese  is  a  hard  metal,  very  much  like  iron. 

The  maximum  positive  valence  of  this  group  is  seven,  and  this  is 
exhibited  in  such  compounds  as  KC1O4,  KBr04,  and  KC1O4.  It  is  not 
out  of  place  to  mention  that  manganese,  with  all  its  irregularities, 
alap,  shows  the  true  group  valence  in  the  salt  KMnCX.  It'  should  be 
noted  also  that  the  positive  activity  of  the  group  elements  increases 
from  fluorine  to  iodine.  Fluorine  forms  no  oxygen  acids,  and  iodine 
displaces  the  other  halogens  from  the  chlorates,  bromates,  and  other 
oxygen  salts. 

The  negative  valence  of  the  group  is  one,  as  shown  in  HF,  HC1, 
HBr,  and  HI.  Here,  of  course,  the  displacing  order  is  in  the  reverse 
direction. 

Group  8. — In  this  case  we  have  no  conseculive  column  arrangement, 
but  three  horizontal  lines  of  three  elements  each,  each  line  forming  a 
transition  between  the  first  and  second  series  of  a  long  period. 

The  first  three,  iron,  cobalt,  and  nickel,  stand  between  manganese 
on  the  one  hand  and  copper  on  the  other.  This  is  a  very  natural  position 
for  them,  since  iron  is  much  like  manganese,  and  nickel,  especially  in 
its  salts,  is  much  like  copper.  The  second  trio,  ruthenium,  rhodium, 
and  palladium,  form  the  same  sort  of  transition.  The  neighbor  on  the 
left  is  here  missing,  but  on  the  right  comes  silver,  the  close  neighbor  of 
palladium.  The  third  transition  group  includes  osmium,  iridium,  and 
platinum,  standing  between  an  unknown  element  on  one  side  and  gold 
on  the  other.  These  three  elements  are  distinguished  for  their  great 
density.  Osmium  has  a  density  of  22.5,  the  highest  of  any  known 
substance. 

The  maximum  positive  valence  of  this  group  is  eight.  This  seems 
to  be  exhibited,  however,  in  only  two  cases,  namely,  in  the  compounds 
OsOi  and  RuO4.  This  group  shows  no  negative  valence  at  all;  in  other 
words,  the  negative  valence  is  zero. 


PREDICTION  OF  PROPERTIES  103 

Prediction  of  Properties. — One  of  the  most  valuable  attributes  of  the 
Periodic  System  is  the  fact  that  it  enables  us  to  predict  the  properties 
of  any  element,  known  or  unknown.  At  the  time  when  the  system  was 
presented,  Mendeleeff  predicted  the  properties  of  several  elements 
then  unknown.  Some  of  these  were  afterwards  discovered,  and  the 
observed  properties  corresponded  with  those  predicted  almost  to  the 
letter.  Two  of  these  elements  were  gallium  and  scandium. 

The  method  is  simple:  Since  the  properties  of  the  elements  are,  in 
general,  functions  of  their  atomic  weights  (or  atomic  numbers)  changes 
in  these  properties  will  not  be  abrupt,  but  gradual;  and  the  properties 
of  any  given  element  will,  in  general,  be  closely  related  to  those  of  its 
neighbors.  The  most  immediate  neighbors  an  element  has  are  its 
analogues  in  the  same  sub-group  and  those  immediately  to  right  and  left 
in  the  same  series.  To  these  we  should  look  for  suggestions.  More- 
over, in  our  discussion  of  periodic  functions  and  group  characteristics 
we  have  tried  to  show  the  general  trend  of  relations  all  through  the  sys- 
tem. The  following  generalizations  may  be  observed: 

The  groups  all  start  with  two  elements,  the  second  of  which  is  the 
more  accurate  group  type.  Below  these  we  always  have  two  sub-groups,  - 
the  left  (A)  more  basic  than  the  right  (B).  Among  groups  1—4  sub-- 
group A  shows  the  true  group  correspondence;  beyond  group  4  it  is 
sub-group  B.  The  elements  of  sub-group  B  in  the  early  groups  are 
heavy  useful  metals;  in  the  later  groups  they  are  non-metallic. 

The  maximum  positive  valence  increases  uniformly  from  group  to 
group,  the  numerical  value  being  the  same  as  the  group  number.  We 
may  look  for  positive  valences  lower  than  the  maximum,  first  in  sub- 
group B  and  later  in  both  sub-groups.  In  group  4,  negative  valence 
appears  and  there  equals  the  positive  valence  (four).  From  there  on, 
it  decreases  group  by  group,  until  in  group  8  it  becomes  zero.  Negative 
valence  appears  only  in  the  type  elements  and  in  sub-group  B. 

Elements  to  the  left  are  basic;  the  property  becomes  indifferent 
in  group  4 ;  beyond  4,  elements  become  more  and  more  acidic.  Basicity 
generally  increases  down  through  each  group,  particularly  in  sub-group 
A,  although  in  sub-group  B  of  groups  1-4  basicity  decreases  with 
increasing  atomic  weight,  a  reversal  of  the  regular  order.  If  the  type 
member  of  a  group  is  amphoteric,  a  member  far  down  the  A  side  will  be 
basic.  Valence  lower  than  the  group  valence  is  accompanied  by  a  more 
basic  nature. 

Positive  displacing  power  follows  the  same  order  as  basicity:  indeed 
it  is  only  another  way  of  naming  the  same  property. 

Elements  of  the  sixth  period  are  radioactive. 

In  application  of  these  general  principles  let  us  attempt  to  predict 
the  properties  of  the  element  germanium: 


104    CLASSIFICATION  OF  ELEMENTS:  THE  PERIODIC   SYSTEM 

(1)  The  atomic  weight  will  be  about  72.5,  the  mean  of  those  of 
gallium  (70)  and  arsenic  (75). 

(2)  It  will  be  a  white  metal,  stable  in  the  air. 

(3)  The  maximum  positive  valence  will  be  four;  the  principal  oxide 
will  be  GeC>2.     It  may  form  a  hydride,  GeILt,  probably  not,  since  tin 
does  not.     It  will  also  show  a  positive  valence  of  two  and  a  corresponding 
oxide,  GeO. 

(4)  It  will  be  amphoteric,  the  oxides,  dissolving  in  both  acids  and 
bases.     The  higher  oxide  will  be  more  acidic. 

(5)  The  melting  point  will  be  much  higher  than  that  of  tin,  perhaps 
800°  C. 

(6)  It  should  displace  tin  from  its  salts  or  at  least  reduce  stannic 
tin  to  stannous.     Zinc  will  displace  it,  as  it  does  tin  and  lead.     It  should 
barely  dissolve  in  HC1. 

(7)  It  will  give  a  chloride  which  is  a  heavy  fuming  liquid. 

(8)  Like  tin,  it  should  give  a  yellow  sulphide,  insoluble  in  dilute 
acids  but  soluble  in  ammonium  sulphide. 

The  following  are  the  actual  properties  as  far  as  they  are  known, 
the  numbers  corresponding : 

(1)  Atomic  weight,  72.5. 

(2)  Grayish-white  metal,  stable  in  the  air. 

(3)  Gives  two  oxides,  GeC>2  and  GeO.     The  hydride  GeH4  is  known. 

(4)  It  is  amphoteric,  the  oxides  dissolving  in  both  acids  and  bases. 
The  higher  oxide,  GeC>2,  is  soluble  in  water,  and  the  solution  has  a  sour 
taste. 

(5)  The  melting  point  is  900°  C. 

(6)  Zinc  displaces  it  in  acid  solution.     No  data  as  to  its  displacing 
power  with  tin.     It  does  not  dissolve  in  HC1. 

(7)  The  chloride  is  a  colorless,  fuming  liquid  of  density  1.88,  very 
much  like  TiCU  and  SnCU. 

(8)  It  gives  a  white  sulphide,  GeS2,  insoluble  in  dilute  acids,  soluble 
in  ammonium  sulphide. 

Other  Forms  of  Periodic  Arrangement. — Since  the  development  of 
the  tabular  form  of  the  Periodic  System  other  forms  have  come  into 
use  also.  The  scope  of  this  chapter  does  not  allow  us  to  present  these  in 
detail,  but  we  may  mention  two  which  have  become  prominent.  One 
is  by  Soddy  and  the  other  by  Harkins.  Both  arrange  the  elements  on  a 
continuous  spiral.  Soddy  gives  the  short  periods  a  single  turn  each, 
thus,  one  turn  from  helium  to  neon,  and  another  turn  from  neon  to  argon. 
For  the  double  periods  a  double  turn,  like  a  figure  8,  is  used.  The  rare 
earths  are  placed  on  a  loop  in  the  main  spiral  between  cerium  and 
tantalum.  Harkins  uses  single  turns  for  the  single  periods  and  double 


EXERCISES  105 

turns  for  the  double  periods ;  but  the  turn  holding  the  second  series  of  a 
double  period  is  placed  inside  the  turn  holding  the  primary  series. 
Isotopes  (and  the  rare  earths)  are  placed  on  the  vertical  rods  supporting 
the  spirals.* 

EXERCISES 

1.  Give  an  outline  of  early  attempts  to  classify  the  elements. 

2.  Who  originated  the  modern  periodic  arrangement?     How  did  their  scheme 
resemble  and  differ  from  Newlands'? 

3.  Describe  the  system  as  it  now  appears,  covering  the  topics:   first  and  second 
periods  with  gradation  of  properties;   the  placing  of  the  symbols  to  indicate  degree 
of  basicity;   arrangement  of  the  third  period;   the  fourth  and  fifth  periods  with  the 
rare  earths;   the  sixth  period;   the  gaps;   the  increment  in  the  atomic  weights  with 
approximate  relation  between  atomic  weight  and  atomic  number;  the  transpositions. 

4.  Discuss  the  position  of  hydrogen  in  the  Periodic  System. 

5.  Discuss  the  valence  relations  seen  in  the  Periodic  System.     What  is  Abegg's 
rule? 

6.  Show  the  periodic  nature  of  the  acid-  and  base-forming  tendency  of  the 
elements,  covering  each  group  in  succession  and  giving  examples. 

7.  Discuss  the  atomic  volume  graph,  showing  the  position  of  certain  types  of 
elements. 

8.  Name  the  first  two  members  of  each  group  from  0  to  7,  and  show  which  member 
in  each  case  is  more  typical  of  the  group. 

9.  Name  the  elements  comprising  sub-groups  A  and  B  in  groups  1  and  2. 

10.  Point  out  the  gradation  of  the  following  properties  in  Group  1,  A  and  B: 
density;   atomic  volume;   melting  point;   boiling  point;   valence;  hardness;   action 
on  water  and  strength  of  hydroxides;  displacing  power;  occurrence. 

11.  How  do  the  properties  of  the  elements  of  Group  2  differ  from  those  of  Group  1? 
What  likenesses  do  you  find? 

12.  How  does  change  of  valence  affect  the  nature  of  an  element?     Examples. 

13.  In  what  group  does  negative  valence  appear?    In  what  sub-group?    Examples. 

14.  Discuss  the  matter  of  group  correspondence  in  Group  1,  Group  4,  and  Group  7. 

15.  Give  examples  illustrating  the  positive  and  negative  valence  of  Group  6. 

16.  Discuss  the  nature  of  the  two  hydroxides  SO2(OH)2  and  UO2(OH)2.      Which 
should  be  the  more  basic^^Why? 

17.  What  are  the  characteristics  of  Group  8? 

18.  Give  general  statements  concerning    the  gradation  seen  in  the    following 
properties:  group  correspondence;  valence;  acid  and  basic  nature;   melting  point; 
positive  and  negative  displacing  power. 

19.  Show  how  and  with  what  success  nine  properties  of  the  element  germanium 
can  be  predicted. 

20.  Predict  the  properties  of  the  missing  alkali  and  the  missing  halogen. 

21.  Describe  the  periodic  arrangements  of  Soddy  and  Harkins. 

*  A  good  cut  and  description  of  Soddy's  arrangement  may  be  found  in  his  book, 
"  Chemistry  of  the  Radio  Elements."  Harkins'  scheme  is  illustrated  and  described 
in  McCoy  and  Terry,  pp.  563-566.  See  also  Harkins'  original  paper,  Jour.  Am. 
Chem.  Soc.,  38,  169. 


CHAPTER  X 


RAYS    FROM    VACUUM    TUBES,    RADIOACTIVITY,    ATOMIC 

DISINTEGRATION 

Rays  from  Vacuum  Tubes. — As  early  as  1874,  Sir  William  Crookes,* 
an  English  chemist,  discovered  that  high-tension  currents  of  electricity 
were  able  to  pass  through  tubes  containing  gases  under  very  low  pres- 
sure. He  noted  the  strange  glow  filling  the  tubes  and  found  that  an 
object  placed  inside  cast  a  shadow  on  the  glass  wall  opposite.  He 
explained  the  phenomenon  as  the  projection  from  the  cathode  of  nega- 
tively charged  particles  having  a  long  free  path  and  very  high  kinetic 


FIG.  6. — X-ray  Apparatus. 

energy.  For  twenty  years,  Crookes'  tubes  were  used  for  demonstration 
purposes  before  the  discovery  was  made  that  anything  was  occurring 
outside  the  tube.  In  1895  Roentgen,  f  a  German  physicist,  found  by 
accident  that  some  form  of  radiation  was  coming  through  the  glass  walls 
which  was  able  to  affect  a  photographic  plate.  Not  knowing  what 
this  radiation  was  he  gave  it  the  appropriate  name  of  "  X-rays."  Since 
that  time,  much  study  has  been  put  on  all  the  phenomena  connected 
with  vacuum  tubes,  both  internal  and  external,  and  from  them  the 
modern  X-ray  tubes  have  been  developed.  The  above  sketch  repre- 

*  Sir  William  Crookes  (1832-1921).  Famous  English  chemist  and  physicist. 
Editor  of  Chemical  News. 

t  William  Conrad  Roentgen  (1845-  ),  Professor  of  Physics,  University  of 
Munich. 

106 


RAYS  FROM  VACUUM  TUBES  107 

sents  a  rather  common  form  of  X-ray  apparatus.  The  tube  is  con- 
structed of  glass  with  sealed-in  metallic  electrodes,  as  seen.  The  gas 
pressure  inside  the  tube  is  about  0.001  mm.  A  high-tension  current 
is  led  in  through  the  anode,  A,  and  passes  out  through  the  cathode,  C. 
When  the  apparatus  is  in  action  a  strange  bluish  glow  seems  to  fill  the 
bulb,  and  X-rays  (invisible)  radiate  out  from  the  target  or  ante- 
cathode,  Ac. 

The  rays  produced  inside  an  X-ray  tube  consist  of  three  types : 
First  there  are  the  anode  rays,  which  consist  of  positively  charged 
atoms  of  the  residual  gas  in  the  tube.  These  rays  have  also  been  called 
"  canal  rays  "  from  the  fact  that  they  are  usually  made  to  pass  through 
a  small  opening,  or  canal,  in  the  cathode  plate  in  order  that  they  may 
be  isolated  from  the  other  rays  produced  simultaneously.  These  rays, 
consisting  as  they  do  of  relatively  large  particles,*  are  relatively  slow 
moving.  Their  actual  speed,  however,  is  governed  somewhat  by  the 
intensity  of  the  potential  applied.  Their  positive  nature  was  demon- 
strated by  the  direction  in  which  they  were  deflected  by  a  strong 
electrical  field. 

The  second  kind  of  rays  from  a  vacuum  tube  are  the  so-called 
cathode  rays.  These  rays  have  been  thoroughly  investigated  f  by  such 
men  as  Lenard,  Perrin,  Hertz,  {  and  J.  J.  Thomson.  §  By  noting  the 
direction  of  deviation  in  the  electric  field,  Thomson  found  them  to  be 
negatively  charged,  and  from  their  undoubted  particulate  character  he 
named  them  "  corpuscles."  Johnstone  Stoney  afterwards  applied  to 
them  the  name  "  electrons,"  and  this  name  has  now  come  into  general 
use.  The  speed  of  the  cathode  particles  also  varies  with  the  applied 
potential,  but  in  any  case  it  is  much  greater  than  that  of  the  anode 

*  In  order  to  shorten  the  discussion  we  shall  find  it  necessary  to  make  some 
seemingly  dogmatic  statements  concerning  speeds,  magnitudes,  etc.;  but  it  should 
be  understood  that  all  these  values  have  been  accurately  measured  by  well-known 
physical  methods,  whether  or  not  this  is  stated.  Some  of  these  methods  will  be 
found  described  in  the  following  books: 

Rutherford,  Radioactive  Substances  and  their  Radiations  (1913). 

Raffety,  Introduction  to  the  Science  of  Radioactivity  (1909). 

Soddy,  Radioactivity. 

Duncan,  New  Knowledge  (1905). 

Thomson  and  others,  several  good  articles  in  Scientific  American  Supplement, 

Vols.  83  and  84. 

t  For  a  good  historical  account  see  Rutherford,  Radioactive  Transformations, 
Chapter  I  (1906). 

JHeinrich  Rudolph  Hertz  (1857-1894),  Professor  of  Physics,  University  of 
Bonn.  Discovered  "wireless"  waves. 

§  Joseph  John  Thomson,  Professor  of  Physics,  University  of  Cambridge.  Brilliant 
investigator  of  atomic  structure. 


108  RAYS  FROM  VACUUM  TUBES,  RADIOACTIVITY 

particles.  This  is  due  undoubtedly  to  their  much  smaller  mass.  Thom- 
son found  the  actual  speeds  to  vary  from  10,000  to  100,000  miles  per 
second,  thus  approaching  the  velocity  of  light.  The  ratio  of  the  charge 
to  the  mass  (e/m)  was  found  to  be  1845  times  as  great  as  in  the  case  of 
the  hydrogen  ion;  and  since,  as  was  later  found,  the  charge  is  the  same 
in  magnitude  although  opposite  in  sign,  the  mass  must  be  1/1845  that 
of  the  hydrogen  atom.  We  should  note  here,  however,  that  the  mass 
thus  found  is  only  an  average  value.  The  surprising  thing  about  the 
whole  matter  is  that  the  mass  of  an  electron  is  found  to  vary  with  the 
speed.  This  has  led  to  the  important  conclusion  that  the  electron  is 
entirely  electrical  in  nature — not  a  particle  of  matter  plus  an  electrical 
charge,  but  simply  an  electrical  charge.  The  actual  value  of  the  elec- 
tronic charge  has  been  most  accurately  determined  by  Millikan,* 
and  has  been  found  to  be  4.774  XIO"10  electrostatic  units  (=1.59X 
10~19  coulombs). 

The  third  kind  of  rays  from  a  vacuum  tube  are  called  X-rays  (or 
Roentgen  rays  from  the  name  of  the  discoverer).  They  are  produced 
whenever  the  swiftly  moving  cathode  rays  are  suddenly  stopped  by 
striking  some  object.  Thus  in  the  sketch  above,  the  cathode  rays  are 
shown  (they  are  invisible,  of  course)  as  focused  on  the  center  of  the  anti- 
cathode;  from  this  point  the  X-rays  radiate  out.  They  are  not  particu- 
late  in  character,  but  are,  rather,  electromagnetic  waves  of  the  same 
nature  as  light  but  of  much-  shorter  wave  length.  Millikan  has  shown 
that  if  the  ultra-violet  spectrum  is  extended  forward  to  the  shorter  wave 
lengths  and  the  X-ray  spectrum  is  extended  backward  to  the  longer 
wave  lengths  the  same  lines  appear  in  both.  This  shows  the  con- 
tinuity of  the  whole  series  and  proves  absolutely  that  visible  light  rays, 
ultra-violet  rays,  and  X-rays  are  all  manifestations  of  the  same 
phenomenon. 

X-rays  possess  most  remarkable  powers.  They  are  able  to  penetrate 
matter  of  various  kinds,  such  as  wood,  flesh,  etc.  They  are  the  only 
rays,  for  example,  that  pass  through  the  glass  walls  of  the  X-ray  bulb. 
They  easily  affect  a  photographic  plate,  and,  because  of  the  fact  that 
some  kinds  of  matter,  notably  metals  and  bones,  are  less  permeable  to 
them,  shadow  pictures  of  such  objects  can  be  made  by  their  use.  The 
common  use  of  X-ray  machines  in  dentistry  and  surgery  makes  any 
further  description  of  this  property  unnecessary.  Another  strange 
property  is  their  ability  to  produce  what  is  called  "  ionization  "  in  gases. 
The  atoms  of  gases  contain  positively  charged  particles  together  with  a 
sufficient  number  of  electrons  to  balance  these  positive  charges.  The 
intense  jar  or  vibration  caused  by  the  X-rays  results  in  the  actual 
*  See  account  in  Professor  Millikan's  book,  The  Electron. 


SOME  SPECIAL  POINTS  CONCERNING  ELECTRONS  109 

expulsion  of  one  or  more  electrons  from  an  atom,  leaving  the  atom  wi\,h 
an  excess  positive  charge.  Such  an  atom  is  then  able  to  take  up  elec- 
trons from  any  available  source  and  is  thus  able  to  discharge  an  electro- 
scope, for  example.  This  ionizing  power  is  shared  to  some  extent  by 
the  cathode  rays. 

Some  Special  Points  Concerning  Electrons. — Faraday,*  in  his 
electrical  experiments  on  solutions,  found  that  a  gram-atomic  weight 
of  any  univalent  ion  always  carried  the  same  quantity  of  electricity, 
while  a  gram-atomic  weight  of  a  bivalent  ion  always  carried  exactly 
twice  as  much,  etc.  As  early  as  1874,  Stoney  showed  that  such  facts 
as  these  must  indicate  that  electricity  was  granular  in  nature,  that  is, 
made  up  of  minute,  but  like  quantities.  Our  modern  study  of  vacuum- 
tube  phenomena  and  radio-activity  has  now  made  it  certain  that 
Stoney  was  right  and  that  the  minute  negative  charges  called  electrons 
are  the  fundamental  units  of  movable  electricity.  There  may  be  a 
unit  of  positive  electricity  also,  but  so  far  we  have  probably  not  been 
able  to  isolate  it. 

What  we  call  an  electric  current,  it  is  now  believed,  is  merely  a  move- 
ment of  electrons  through  a  wire.  We  have  mentioned  the  fact  that  the 
atoms  of  any  substance  contain  these  electrons  as  an  important  part 
of  their  structure.  Now,  it  happens  that  in  some  cases,  notably  those  of 
copper,  silver,  gold,  and  most  other  metals,  there  seem,  to  be  a  good 
many  electrons  among  the  atoms  which  are  very  loosely  held.  If  some 
of  these  electrons  are  removed  from  one  end  of  a  wire  by  application 
of  what  we  call  "  potential  "  the  natural  repulsion  of  the  other  electrons 
for  each  other  seems  to  cause  them  to  rush  into  the  vacancy,  thus 
causing  a  general  motion  through  the  wire.  What  we  call  a  non- 
conductor is  probably  a  substance  which  contains  very  few  free  electrons. 

Free  electrons  are  undoubtedly  responsible  for  many  other  phe- 
nomena also.  Thus  it  is  a  well-known  fact  that  rubbing  a  glass  rod 
with  a  piece  of  silk  gives  the  silk  a  negative  charge  and  the  glass  a 
positive  charge.  This  is  explained  by  supposing  that  a  few  free  electrons 
on  the  surface  of  the  glass  were  simply  rubbed  off  by  the  silk. 

Charging  by  induction  is  easily  explained  also  by  use  of  the  electron 
theory.  When  a  rod  holding,  say,  a  negative  charge,  is  brought  near  the 
end  of  a  neutral  rod,  the  end  of  the  rod  near  the  first  is  always  found 
with  a  positive  charge  and  the  opposite  end  with  a  negative  charge. 
This  is  explained  by  assuming  that  the  free  electrons  on  the  second  rod 
are  repelled  by  those  on  the  first,  and  so  scurry  away  to  the  opposite  end. 

Lightning  is  now  believed  to  be  purely  an  electronic  phenomenon. 

*  Michael  Faraday  (1791-1867),  Professor  of  Chemistry  in  the  Royal  Institution, 
London.  Noted  for  his  splendid  work  on  electrolysis,  and  other  electrical  phenomena. 


110  RAYS  FROM  VACUUM   TUBES,   RADIOACTIVITY 

It  seems  that  the  electrons  themselves,  or  molecules  of  air  carrying  an 
extra  electron  or  two  (negative  ions),  form  good  nuclei  around  which  the 
moisture  in  the  air  may  start  to  condense.  When  the  droplets  thus 
formed  grow  large  enough  to  fall  as  raindrops  they  evidently  carry 
down  to  the  earth  countless  numbers  of  these  stray  electrons.  In  this 
way  a  tremendous  potential  is  finally  developed,  and  the  situation  is 
then  relieved  by  the  passage  of  a  "  stroke  of  lightning  "  between  the 
earth  and  the  cloud. 

^>3o  much  for  electronic  phenomena :  we  now  wish  to  present  a  simple 
description  of  Professor  Millikan's  method  of  determining  the  electronic 
charge*  This  is  important,  since  the  method  and  the  results  attained 
constitute  one  of  our  masterpieces  of  scientific  research.  It  had  been 
supposed  for  thirty  years  or  more  that  electricity  was  granular  in  nature, 
and  the  unit  charge  had  been  determined  in  a  rough  way ;  but  it  remained 
for  Millikan  to  prove  that  electricity  is  granular,  that  the  electron  is 
the  unit  quantity,  and  to  determine  the  electronic  charge  with  an 
accuracy  hitherto  unapproached. 

The  sketch  below  gives  a  fairly  correct  idea  of  the  essential  parts  of 
Professor  Millikan's  apparatus. 

The  procedure  was  essentially  as  follows:  A  fine  spray  of  minute 
oil  drops  was  thrown  into  the  upper  part  of  the  apparatus  by  means  of 
the  atomizer,.  A .  These  tiny  droplets  slowly  settled  toward  the  bottom 
of  the  compartment,  and  finally  one  of  them  passed  through  the  pin  hole, 
P,  into  the  lower  compartment,  as  could  be  seen  through  the  telescope, 
T.  The  hole  was  then  closed  to  exclude  other  droplets,  and  the  given 
droplet  was  taken  under  observation  through  the  telescope,  being  made 
visible  by  means  of  a  strong  light  coming  in  from  the  side  (not  shown  in 
the  diagram).  Because  of  the  force  of  gravitation,  the  droplet  slowly 
fell.  The  rate  of  fall  was  uniform,  not  accelerated,  on  account  of  the 
minuteness  of  the  droplet  and  the  viscosity  of  the  air.  (We  note 
the  same  thing  in  the  fall  of  a  parachute  or  of  the  motes  in  the 
air.)  The  actual  velocity  was  about  one  millimeter  per  second,  and 
could  be  accurately  measured  by  means  of  a  stop-watch  and  a  cross- 
hair device  in  the  telescope.  When  the  speed  of  the  droplet  had  been 
measured,  and  the  droplet  was  nearing  the  plate  N,  a  few  electrons  were 
set  free  inside  the  chamber  by  means  of  the  X-ray  tube  0  (ionizing 
effect).  At  the  same  time  the  plates  M  and  N  were  oppositely  charged 
by  means  of  a  strong  battery,  the  upper  plate  positively  and  the  lower 
negatively.  After  a  moment,  one  or  more  electrons  attached  themselves 
to  the  oil  droplet,  and  the  latter  was  then  seen  to  stop  suddenly  in  its 
downward  course  and  move  slowly  upward.  When  it  came  close  to  M 

*  For  Professor  Millikan's  own  account  of  the  work,  see  his  book,  The  Electron. 


SOME  SPECIAL  POINTS  CONCERNING  ELECTRONS 


111 


the  electric  field  was  switched  off,  and  the  droplet  again  allowed  to  fall. 
The  droplet  always  fell  at  the  same  rate  as  when  uncharged,  this  being 
due  to  the  extremely  small  mass  of  the  attached  electron.  Thus  the 
droplet  could  be  made  to  make  hundreds  of  trips,  upward  with  field  on, 
downward  with  field  off,  and  the  speed  could  be  measured  each  time. 
The  speed  downward  was  always  the  same,  and  the  speed  upward 
varied  with  the  number  of  electrons  attached  to  the  droplet.  From 
the  downward  speed  and  the  known  viscosity  of  the  air  the  gravitational 
pull  on  the  droplet  could  be  calculated.  From  the  upward  speed,  the 


FIG.  7. — Diagram  of  Millikan's  Apparatus  for  the  Determination  of  the  Electronic 

Charge. 

viscosity,  the  gravitational  pull,  and  the  known  electrical  potential,  the 
magnitude  of  the  electronic  charge  could  be  calculated. 

Millikan  found  that  the  charge  on  the  droplet  was  invariably  either 
identical  with  the  smallest  charge  ever  found  or  an  exact  multiple  of  it 
by  a  whole  number,  depending,  of  course,  on  the  number  of  electrons 
attached.  Among  the  thousands  of  observations  actually  made  not  a 
single  exception  to  this  rule  was  found. 

These  experiments  prove  beyond  the  shadow  of  a  doubt  that  elec- 
tricity exists  in  granules,  and  that  the  electron  is  the  unit  granule. 
Millikan's  value  for  the  electronic  charge,  calculated  as  above  described, 
was  4.774X  10~10  electrostatic  units,  with  a  probable  error  of  0.2  per  cent. 
We  may,  therefore,  place  this  number  among  the  accurately  determined 
and  perfectly  dependable  constants  of  chemistry  and  physics. 


112  RAYS  FROM  VACUUM   TUBES,   RADIOACTIVITY 

Discovery  of  the  Radioactive  Elements. — The  discovery  of  radium 
and  the  other  radioactive  elements  is  a  charming  story  which  should 
be  read  by  everyone,  but  which  we  have  not  the  space  to  cover  ade- 
quately here.  We  shall  give  the  merest  outline.* 

Becquerelj  found  (1896)  that  certain  uranium  salts  gave  off  rays  which 
could  affect  a  photographic  plate,  even  when  it  was  inside  the  holder,  and 
which  had  other  remarkable  powers.  At  his  suggestion,  Madame  Curie  t 
studied  uranium  minerals  and  found  them  more  active  than  the  pure 
uranium  salts.  Even  the  residues  of  uranium  minerals  from  which  all  the 
uranium  had  been  removed  were  much  more  active  than  uranium 
itself.  These  facts  led  to  the  belief  that  the  activity  was  due,  mainly 
at  least,  to  the  presence  of  a  new  element.  With  this  in  mind,  Madame 
Curie  worked  up  something  over  a  ton  of  uranium  residues,  separating 
them  by  the  well-known  methods  of  qualitative  analysis.  Her  first 
important  discovery  was  an  element  associated  with  bismuth,  which 
she  called  Polonium  in  honor  of  her  native  land,  Poland.  Later  she 
found  another  active  element  associated  with  barium.  This,  by  a  happy 
choice,  she  called  radium.  Radium  was  so  much  like  barium  that  it 
was  only  by  a  long,  tedious  process  of  fractional  crystallization  of  salts 
that  she  finally  obtained  a  radium  compound  in  pure  form.  This  was 
finally  done,  however,  and  most  of  the  properties  of  the  element,  includ- 
ing its  atomic  weight,  were  determined.  The  atomic  weight  was  found 
to  be  226;  and  this,  together  with  the  common  properties  of  the  element, 
placed  it  at  the  bottom  of  the  alkaline  earth  group  in  the  Periodic 
System.  The  radioactivity  of  the  pure  radium  compound  was  found 
to  be  nearly  two  million  times  as  great  as  that  of  an  equal  amount  of 
pure  uranium  salt. 

Besides  the  new  radioactive  elements,  radium  and  polonium,  the 
long-known  elements,  uranium  and  thorium,  also  show  decided  radio- 
active qualities.  In  addition  to  these  there  are  actinium  and  ionium, 
discovered  soon  after  radium,  and  also  a  considerable  number  of  more 
or  less  fleeting  elements  which  we  shall  consider  later. 

Rays  from  Radioactive  Substances. — The  rays  from  radioactive 
substances  are  of  three  types,  strikingly  analogous  to  the  three  types  of 
rays  from  vacuum  tubes;  First  there  are  the  a  §  rays,  so-called,  which 

*  For  more  comprehensive  treatment  see  Rutherford,  Radioactive  Transfor- 
mations. 

f  Henri  Becquerel  (1852-1908),  Professor  of  Physics,  National  Museum  of 
Natural  History,  Paris. 

t  Marie  Sklodowska  Curie,  Professor  of  Physics  at  the  Sorbonne,  Paris.  See 
Harrow,  Eminent  Chemists  of  Our  Time,  p.  155. 

§  Pronounce,  "  alpha." 


RAYS  FROM  RADIOACTIVE  SUBSTANCES  113 

correspond  in  a  way  to  the  canal  rays  from  a  vacuum  tube.  The  main 
differences  are  the  fact  that  the  a  rays  always  consist  of  particles  of  the 
same  size,  and  that  their  speeds  are  enormously  greater.  Rutherford  * 
has,  in  a  recent  article,  f  stated  in  a  striking  way  the  nature  and  some  of 
the  remarkable  properties  of  the  a.  particles.  They  consist  always,  he 
says,  of  helium  atoms,  each  carrying  two  unit  positive  charges  of  the 
same  magnitude  as  that  carried  by  the  electron.  This  must  be  true, 
because  it  is  possible  to  transform  a.  rays  into  helium  gas  by  simply 
attaching  electrons.  The  particles  are  shot  off  from  their  radioactive 
parent  at  a  speed  of  about  19,000  kilometers  per  second  (20,000  times 
the  speed  of  a  rifle  bullet) .  One  ounce  of  a  particles,  thus  moving,  would 
strike  with  the  same  energy  as  10,000  tons  of  solid  shot  moving  with  a 
speed  of  1  kilometer  (0.62  mile)  per  second.  They  strike  a  screen  of 
zinc  sulphide  (a  fluorescent  substance)  with  such  force  as  to  cause  flashes 
of  light.  J  They  tear  through  7  cm.  of  air  at  ordinary  pressure  before 
they  come  to  a  stand,  passing  thus  right  through — not  between — 
countless  numbers  of  molecules.  In  doing  this,  they  knock  out  from 
these  molecules  some  of  the  contained  electrons,  leaving  them  with  an 
excess  positive  charge,  and  thus  making  them  able  to  conduct  the 
charge  away  from  an  electroscope  (ionization) . 

Due  to  their  large  size  the  a  particles  have  little  power  to  penetrate 
solid  matter;  a  thin  sheet  of  metal  easily  cuts  them  off,  although  sheets 
of  metal  can  be  made  sufficiently  thin  to  allow  them  to  pass. 

C.  T.  R.  Wilson  has  found  a  very  clever  method  of  making  the 
track  of  the  a  particles  visible.  He  directs  the  particles  into  an  atmos- 
phere supersaturated  with  water  vapor.  The  ions  formed  act  as 
nuclei  around  which  tiny  droplets  of  water  condense,  thus  producing  a 
thin  line  of  fog  as  far  as  the  particle  goes.  This  line  of  fog  is  photo- 
graphed, and  thus  the  track  of  the  a  particle  is  made  a  permanent  and 
visible  thing  (Fig.  8,  p.  114). 

The  second  kind  of  rays  coming  from  radioactive  substances  are  the 
so-called  ft  §  rays.  These  are  identical  in  every  way  with  the  cathode 
rays,  except  that  they  are  more  penetrating.  This  is,  of  course,  due  to 
their  much  greater  speed.  A  sheet  of  metal  of  sufficient  thickness  to 
cut  off  all  the  ordinary  cathode  rays  leaves  the  ft  rays  practically  unaf- 

*  Sir  Ernest  Rutherford  (1871-  ),  Professor  of  Physics,  University  of  Cam- 
bridge, England;  formerly  Professor  in  McGill  University,  Montreal. 

t  Science,  Nov.  21,  1919. 

t  Sir  William  Crookes  has  invented  an  instrument,  called  a  spinthariscope,  in 
which  the  flashes  caused  by  the  a  particles  bombarding  a  zinc  sulphide  screen  are 
viewed  through  a  lens. 

§  Pronounce  "  ba  ta." 


114 


RAYS  FROM  VACUUM   TUBES,   RADIOACTIVITY 


fected.  They,  of  course,  possess  the  power  to  affect  a  photographic 
plate  more  intensely  than  the  cathode  rays.  They  can  cause  ionization 
of  gases,  but  are  more  feeble  in  this  respect  than  the  heavier  ft  particles, 
although  their  speed  is  greater. 

The  third  kind  of  rays  from  radioactive  substances  have  been  called 
the  7  *  rays.  They  correspond  to  the  X-rays,  but,  on  account  of  their 
shorter  wave  length  and  greater  frequency,  are  considerably  more 
penetrating.  It  is  important  to  note  that  the  7  rays  never  appear 

except  as  a  concomitant  of  the  < 
swift  ft  particles;  and  when- 
ever ft  particles  are  emitted  7 
rays  will  always  be  found. 
a.  particles  may  be  emitted 
without  any  7  radiation,  but 
swift  ft  particles  never.  The 
relation  between  the  7  impulses 
and  the  /3  particles  is  roughly 
analogous  to  the  relation  be- 
tween the  report  of  a  gun  and 
the  flying  bullet. 

Before  leaving  this  section 
we  must  correct  one  possible 
misapprehension.  We  have 
shown  that  radioactive  rays 
consist  of  three  types:  a  rays, 
ft  rays,  and  7  rays.  It  might 
be  thought  from  this  that 
every  radioactive  substance 

emitted  all  these  rays  at  once.  This,  however,  is  not  the  fact.  Some 
substances  emit  a  rays  alone,  others  emit  ft  and  7  rays,  and  in  only  one 
or  two  cases  does  an  element  emit  all  three.  All  the  more  common 
radioactive  elements,  thorium,  uranium,  and  ionium,  emit  only  a  rays. 
The  ft  and  7  rays  come  from  some  of  the  products  yet  to  be  con- 
sidered. Actinium  is  rayless,  but  it  changes  into  other  substances 
which  emit  rays. 

Radioactive  Emanations. — In  studying  the  radiations  from  thorium 
it  was  early  noticed  that  the  presence  of  air  currents  produced  strange 
effects.  Something  like  a  gas  seemed  to  be  present.  The  product 
could,  for  instance,  be  drawn  through  a  plug  of  cotton,  which  was 
known  always  to  remove  ions  and  rays.  If  a  current  of  air  were  drawn 


FIG.  8. — Fog  Tracks  of  a  Particles  (after 
C,  T,  R,  Wilson.) 


*  Pronounce  "  ga"m  ma." 


RADIOACTIVE  EMANATIONS  115 

over  a  very  active  thorium  compound  its  activity  was  thereby  nearly  all 
removed,  and  the  activity  could  be  detected  in  this  air  at  a  distance. 
If  this  active  air  were  drawn  through  a  tube  immersed  in  liquid  air  the 
active  substance  was  condensed  on  the  walls  of  the  tube,  and  could  be 
recovered  by  warming  the  tube.  The  substance  was  evidently  a  gas; 
and  since  it  seemed  to  come  from  the  thorium,  it  was  named  "  thorium 
emanation.''  This  gas  never  appeared  in  anything  more  than  traces, 
but  its  activity  was  great  and  its  identity  certain.  Like  the  more  com- 
mon radioactive  elements,  it  gave  off  only  a  rays. 

Radium  and  actinium  were  also  found  to  be  accompanied  by  radio- 
active gases,  and  in  these  cases  also  the  gases  were  called  "  emanations." 
Actinium  emanation  occurs  in  very  small  amounts,  and  for  that  reason 
alone  its  properties  could  not  be  accurately  measured.  It  gives  off  only 
a  rays. 

Radium  emanation  has  been  carefully  studied.  Thus,  Gray  and 
Ramsay  *  measured  the  weight  of  a  known  minute  volume  of  the  pure 
gas  by  means  of  a  very  delicate  micro-balance,  and  found  its  molecular 
weight  to  be  222.  It  was  also  found  to  be  inert,  as  far  as  ordinary 
chemical  activity  was  concerned,  and  was  therefore  placed  in  the  zero 
periodic  group.  If,  like  the  other  members  of  the  group,  it  is  monatomic, 
its  atomic  weight  is  also  222,  and  this  puts  it  in  the  same  series  with 
radium,  thorium,  and  uranium.  Radium  emanation  has  lately  been 
named  "  niton  "  and  so  appears  in  the  more  recent  tables.  It  is  interest- 
ing to  note  that  niton  is  the  heaviest  gas  known,  its  density  being  111 
times  as  great  as  that  of  hydrogen.  Even  the  boiling  point  of  this 
extraordinary  gas  is  known,  although  the  largest  amount  ever  handled 
at  any  one  time  has  never  been  over  a  few  cubic  millimeters.  Ruther- 
ford determined  its  boiling  point  by  condensing  the  gas  in  a  small  capil- 
lary tube  placed  vertically  in  a  cooling  bath.  The  temperature  of 
liquefaction  was  determined  by  noting  when  the  phosphorescence,  always 
seen  in  connection  with  the  emanation,  began  to  show  a  greater  intensity 
in  the  lower  end  of  the  tube;  that  is,  when  the  liquid  began  to  form 
there.  The  temperature  of  liquefaction  determined  in  this  way  was 
—65°  C.  Like  the  other  emanations,  radium  emanation  emits  only 
a  rays. 

All  the  emanations  share  one  surprising  property,  namely,  a  short 
life.  They  all  give  off  rays  intensely  when  first  separated  from  the 
parent  compound;  but  after  a  time  the  activity  wanes,  and  the  emana- 

*  Sir  William  Ramsay  (1852-1916)  Professor  of  Chemistry,  University  College, 
London.  Co-discoverer  with  Lord  Rayleigh  of  the  rare  gases  in  the  atmosphere; 
brilliant  investigator  in  radio  chemistry.  For  sketch  of  his  life,  see  Harrow,  loc. 
dt.,  p.  41. 


116  RAYS   FROM   VACUUM   TUBES,   RADIOACTIVITY 

tion  seems  to  be  gone.  Thus  radium  emanation  loses  half  its  original 
activity  in  3.9  days,  the  thorium  emanation  thus  wanes  in  51  seconds, 
and  that  of  actinium  in  4  seconds.  These  intervals  are  spoken  of  as  the 
"  half  periods  "  of  the  active  elements,  or  sometimes  merely  as  the 
"  periods."  The  methods  of  determining  these  periods  will  be  given 
later. 

Along  with  this  fact  about  the  decay  of  the  emanation,  it  should  be 
stated  that  a  new  quantity  of  emanation  is  generated  at  the  same  rate 
at  which  the  old  decays.  Thus,  if  all  the  emanation  is  removed  from  a 
sample  of  radium  salt  by  drawing  air  over  it,  half  the  quantity  removed 
will  be  regenerated  in  3.9  days.  If  a  quantity  of  radium  salt  is  sealed 
up  in  a  tube  and  left  for  a  time,  the  emanation  will  at  first  increase  in 
amount,  but  will  finally  reach  a  maximum  and  then  remain  constant, 
the  rate  of  formation  and  the  rate  of  decay  being  equal.  This  means 
that  in  any  case  the  quantity  of  emanation  present  bears  a  fixed  ratio 
to  the  amount  of  radium. 

Radioactive  Deposits. — As  the  radioactive  emanations  wane  in  power, 
objects  in  the  immediate  neighborhood  become  active.  This  was 
spoken  of  for  a  time  as  "  induced  activity,"  and  was  supposed  to  be  some- 
what like  induced  electric  currents.  It  is  now  known  that  this  activity 
is  due  to  the  formation  of  radioactive  deposits.  These  deposits  have 
been  carefully  studied,  particularly  by  Rutherford,  and  have  been 
shown  to  be  true  solid  radioactive  elements  of  perfectly  definite  identity. 
Their  life  periods  and  some  other  properties  have  been  determined, 
together  with  the  kind  of  rays  they  emit;  and  in  most  cases  even  their 
atomic  weights  are  known  with  a  fair  degree  of  accuracy. 

The  Disintegration  Hypothesis  and  the  Radioactive  Series. — To 
account  for  the  known  facts  of  radioactivity,  such  as  the  emission  of 
rays  and  the  generation  and  decay  of  emanations  and  active  deposits, 
Rutherford  *  and  Soddy  have  developed  a  bold  and  far-reaching 
hypothesis.  They  hold  that  the  atoms  of  all  the  radioactive  elements, 
such  as  uranium,  radium,  thorium,  and  all  the  emanations  and  deposits, 
are  complex  structures  made  up  of  electrons  revolving  around  a  positive 
nucleus.  They  believe  also  that  this  nucleus  itself  contains  both  elec- 
trons and  positive  particles  (perhaps  a  particles)  held  together  under 
great  tension.  Further,  they  believe  that  the  atom  of  the  radioactive 
element  may  become  unstable,  and  may  then  throw  off  either  an  electron 
(/3  ray)  or  a  helium  atom  (a  ray),  leaving  behind  another  element  with 
somewhat  different  properties.  If  the  particle  thrown  off  is  an  electron 
the  atomic  weight  of  the  new  element  will  be  the  same  as  that  of  the 

*  Radioactive  Substances  and  their  Radiations,  p.  344  (1913). 


DISINTEGRATION  HYPOTHESIS  AND  RADIOACTIVE  SERIES     117 

parent,  because  the  electron  is  of  such  exceedingly  small  mass  (1/1845 
|  the  mass  of  the  hydrogen  atom).  If,  on  the  other  hand,  the  particle 
thrown  off  is  a  helium  atom  (atomic  weight  4)  the  atomic  weight  of  the 
new  element  will  be  four  units  lower  than  that  of  the  parent.  Fajans  * 
and  Soddy  f  have  shown  that  the  positive  valence  of  an  element  pro- 
duced by  the  expulsion  of  an  a  particle  must  be  two  less  than  that  of  the 
\  parent,  while  that  of  an  element  produced  by  the  expulsion  of  an  electron 
must  be  one  more  than  that  of  the  parent.  This  can  be  understood 
when  we  remember  that  the  a  particle  takes  away  with  it  two  positive 
charges,  and  that  the  electron  takes  away  a  negative  charge  (or  adds  a 
positive  charge).  The  element  produced  by  expulsion  of  an  a  particle 
should  stand  two  groups  back  of  the  parent  in  the  periodic  system,  due 
to  the  change  in  valence,  while  one  produced  by  expulsion  of  a  ft  particle, 
should  stand  one  group  ahead  of  the  parent.  This  would  be  the  logical 
result  of  the  change  in  valence. 

When  we  accept  the  disintegration  hypothesis,  the  whole  scheme 
of  radioactive  succession  begins  to  take  shape  before  us.  Somewhere 
back  of  radium  is  a  parent  element  which  has  been  breaking  down,  giving 
radium  as  one  of  its  disintegration  products.  Radium,  we  know, 
breaks  down  into  helium  and  niton,  and  niton  in  turn  breaks  down 
into  helium  and  the  active  deposits.  The  parent  (or  grand-parent) 
of  radium  must  be  a  radioactive  element  whose  atomic  weight  is  higher 
than  that  of  radium  and  of  such  a  value  that  a  whole  number  of  a  parti- 
cles may  be  expelled  from  it  and  leave  an  atom  of  radium  with  an 
atomic  weight  of  226.  In  other  words,  the  atomic  weight  of  the  element 
must  be  230,  234,  238,  or  some  number  of  this  series.  We  note  at  once 
that  uranium  answers  this  description  exactly ;  its  atomic  weight  is  238, 
it  is  radioactive,  and  it  is  always  associated  with  radium  in  the  natural 
minerals.  We  may  therefore  regard  uranium  as  the  parent  of  the 
whole  series  of  which  radium  and  niton  are  members.  Thorium,  with 
an  atomic  weight  of  232,  is  the  parent  of  another  series. 

Marvelous  as  it  may  seem,  practically  all  the  individual  members 
of  these  two  radioactive  series  have  been  identified,  and  some  of  their 
important  properties  have  been  noted.  Among  these  are  some  ele- 
ments whose  lives  extend  through  eons  of  years  and  others  whose 
lives  divide  the  tick  of  a  watch  into  a  hundred  parts.  All  the  common 
radioactive  elements  are,  of  course,  included. 

Before  continuing  the  discussion  we  shall  present  the  two  radioactive 
series  as  they  have  now  been  worked  out.  Note  the  following  tables: 

*  Physik.  Z.,  14,  131  (1913). 
t  Chem.  News,  107,  97  (1913). 


118 


RAYS  FROM  VACUUM   TUBES,   RADIOACTIVITY 


The  numbers  inside  the  circles  are  atomic  weights.  The  rays  emitted 
in  each  case,  and  the  life  periods,  are  also  given.  It  is  understood  that 
7  rays  accompany  the  /3. 

Uranium  Series 

Uranium  I    /^"^ 
5  x  10.9  Years  (  238 


Uranium  Y 
2.2  Days 


Uranium  Z 
(Unknown) 


Actinium 


Radio-Actinium 
28.1  Days 

Actinium  X 
16.4  Days 

Actinium  Em. 
5.6  Sec. 


Actinium  A 
0.003  Sec. 


Actinium  B 
52.1  Sec. 


Actinium  C 
3.1  Min. 


Actinium  D 
48  Sec. 


End  Product       . 
Probably  Lead   I210 


End  Product    f  9nR 
Probably  Leadl  205 

FIG.  9. — Uranium  Series  of  Radio-active  Elements. 

We  may  call  attention  to  the  following  points:  The  atomic  weights 
are  calculated  by  subtracting  the  weight  of  a  whole  number  of  a  particles 
from  the  atomic  weight  of  uranium,  and  may  for  that  reason  look  some- 


DISINTEGRATION  HYPOTHESIS  AND  RADIOACTIVE  SERIES     119 


what  speculative.  However,  in  two  cases  at  least,  the  values  can  be 
tested.  These  are  the  cases  of  radium  and  niton.  The  experimental 
value  for  the  atomic  weight  of  radium,  obtained  by  Madame  Curie, 
is  226,  checking  exactly  with  the  calculated  value.  That  of  niton  is 
222.4.  Here  the  concordance  is  not  quite  so  good;  but,  considering  the 
experimental  difficulties  encountered  in  this  determination,  where  a 
few  cubic  millimeters  of  the  gas  were  weighed,  no  very  exact  concordance 


Thorium 
3  x  10  "years 


Thorium  Series 

232 


Meso-Thorium 
7.9  years 

Meso-Thorium  2 
8.9  hrs. 

Radio  Thorium 
2.91  years 

Thorium  X 
5.25  days 


Thorium  C ' 
10-12  sec. 

End  Product 
probably  Lead  V  208 


Thorium  D 
4.5  min. 


End  Product 
208  )  probably  Lead 


FIG.  10. — Thorium  Series  of  Radio-active  Elements. 

is  to  be  expected.  Indeed,  the  calculated  value  may  be,  and  probably 
is,  the  more  nearly  correct.  Considering,  then,  the  agreement  in  these 
two  test  cases,  we  may  consider  it  very  probable  that  the  other  calculated 
values  are  reasonably  correct. 

We  notice  that  ionium  is  the  direct  parent  of  radium,  but  uranium 
is  the  paternal  ancestor  of  the  whole  clan. 

Note  that  radium  could  not  occur  in  the  thorium  series,  because  the 
atom  of  radium,  with  an  atomic  weight  of  226  cannot  be  obtained  from 


120  RAYS  FROM  VACUUM   TUBES,   RADIOACTIVITY 

the  atom  of  thorium,  atomic  weight  232,  by  expulsion  of  a.  particles. 
The  nearest  approach  to  an  atomic  weight  of  226  would  be  224  or  228, 

Two  of  the  elements,  mesothorium  and  actinium,  are  rayless.  Meso- 
thorium  changes  into  mesothorium  2  by  some  internal  rearrangement, 
without  emitting  any  rays.  This  is  shown  by  the  fact  that  when  first 
separated  from  thorium  it  emits  no  rays.  It  is  true  that  rays  begin  to 
appear  after  a  time;  but  these  come  from  a  new  element  evolved  from 
the  old  one;  and  this  element  may  again  be  separated  from  the  rayless  > 
one  by  precipitation  along  with  zirconium  hydroxide,  to  which  it  adheres. 

Note  that  in  two  cases  only  are  both  a  and  0  rays  emitted  from  the 
same  element.  These  are  the  cases  of  thorium  C  and  radium  C.  Note 
also  that  in  both  cases  the  double  ray  activity  results  in  the  formation 
of  two  lines  of  succession,  one  with  unchanged  atomic  weight,  the  other 
with  an  atomic  weight  four  units  lower. 

Radium  F  has  been  found  to  have  the  same  life  period  and  to  emit  the 
same  rays  as  polonium.  The  two  are  probably  identical,  therefore,  and 
one  or  the  other  name  might  be  dropped. 

The  methods  used  in  determining  the  life  periods  are  interesting. 
The  period  for  radium,  for  example,  has  been  determined  by  observation 
of  the  rate  at  which  a  particles  are  given  off.  The  short  periods  can,  of 
course  be  determined  directly  by  noting  the  time  required  for  the  radio- 
active element  to  lose  half  its  activity.  We  have  also  mentioned  the  fact 
that  when  a  radium  compound  is  allowed  to  stand  for  a  time  (forty  days) 
in  a  sealed  tube,  the  amount  of  emanation  reaches  a  maximum  value 
and  then  remains  fixed,  so  that  in  any  case  the  amount  of  emanation 
present  will  bear  a  fixed  ratio  to  the  weight  of  radium.  The  same  thing 
is  true  in  the  case  of  any  of  the  radioactive  elements.  In  an  old  uranium 
mineral,  for  example,  where  the  elements  have  had  perhaps  millions  of 
years  to  come  into  equilibrium,  we  find  these  same  fixed  ratios.  Thus, 
in  every  uranium  mineral,  radium  is  present  in  the  ratio  of  1  gm.  Ra: 
3,000,000  gms.  U.*  Now,  it  is  quite  evident  that  in  any  case  where 
equilibrium  is  established  the  elements  must  be  present  in  amounts  pro- 
portionate to  their  life  periods.  Therefore,  if  we  know  the  period  of 
one  and  the  ratio  of  the  amounts  present,  we  can  at  once  calculate  the 
period  of  the  others.  It  is  interesting  to  note  a  converse  deduction  in 
the  case  of  ionium.  Since  the  life  period  of  that  element  is  about  one 
hundred  times  greater  than  that  of  radium  it  should  be  present  in  any 
uranium  mineral  in  one  hundred  times  the  relative  amount,  and  should 
be  one  hundred  times  less  active. 

Perhaps  one  of  the  most  important  points  to  note  regarding  these 

radioactive  series  is  the  nature  of  the  end-product,  which  seems  to  be 

*  Lind  and  Whittemore,  Jour.  Am.  Chem.  Soc.,  36,  2066. 


EXERCISES 


121 


lead  in  every  case.  We  note,  however,  that  three  different  atomic 
weights  are  involved,  namely,  206,  208,  and  210.  If  these  end-products 
are  really  lead  they  represent  three  isotopic  forms.  We  have  already 
mentioned  the  work  of  Richards  and  Soddy  on  the  atomic  weights  of 
lead  of  radioactive  origin.  Richards  obtained  a  value  for  lead  in 
uranium  minerals  of  about  206,  while  Soddy  obtained  a  value  for  the 
same  element  in  thorium  minerals  of  about  208.  Rutherford  *  thinks 
that  lead  is  almost  surely  the  end-product  in  the  case  of  the  uranium- 
radium  series,  but  has  no  data  regarding  the  actinium  branch  or  the 
thorium  series. 

One  other  point  may  be  mentioned.  We  have  already  explained  that 
an  a-ray  product  should  stand  two  groups  back  of  its  parent  in  the  Peri- 
odic System,  while  a  (3-ray  product  should  stand  one  group  in  advance  of 
its  parent.  Note  now  in  this  connection  that  radium  stands  in  group  2, 
while  its  a-ray  product,  niton,  stands  in  group  0.  Note  also  that  radium 
results  when  uranium  has  given  off  three  a  particles  and  two  /3  particles. 
Uranium  stands  in  group  6.  The  expulsion  of  the  three  a  particles 
should  result  in  a  product  six  groups  back  of  uranium,  that  is,  in  the 
zero  group,  but  the  expulsion  of  the  two  0  particles  should  advance  the 
product  to  group  2,  and  this  is  where  we  actually  find  it.  The  following 
chart  shows  the  changes  occurring  between  uranium  and  niton: 


FIG.  11. — Periodic  Change  Caused  by  Expulsion  of  a  and  ft  Particles. 


EXERCISES 

1.  Describe  the  X-ray  tube.     What  rays  are  emitted  by  it? 

2.  Give  the  properties  of  anode  rays. 

3.  What  are  cathode  rays?     Give  names,  speed,  mass,  nature,  and  electronic 
charge. 

4.  Give  source,  nature  and  properties  of  X-rays. 

6.  Give  evidence  of  the  particulate  character  of    electricity.      What  are  the 
particles? 

6.  What  is  an  electric  current? 

7.  What  is  frictional  electricity? 

8.  Explain  the  process  of  "  charging  by  induction." 

9.  How  is  lightning  produced? 

*  Radioactive  Substances  and  their  Radiations,  p.  596  (1913). 


122  RAYS  FROM  VACUUM  TUBES,   RADIOACTIVITY 

10.  Give  an  accurate  description  of  Professor  Millikan's  method  for  determining 
the  electronic  charge. 

11.  Tell  how  and  by  whom  radium  was  discovered. 

12.  What  are  the  properties  of  radium? 

13.  What  other  radioactive  elements  are  known? 

14.  What  rays  are  emitted  by  radioactive  substances? 

15.  Describe  the  a  rays,  noting  their  nature,  speed,  and  other  properties. 

16.  What  are  j8  rays  and  7  rays?     How  related  to  cathode  rays  and  X-rays? 

17.  How  was  thorium  emanation  discovered?     Properties? 

18.  Describe  radium  emanation,  including  method  of  determining  its  molecular 
weight.     What  is  its  atomic  weight?     Why?     How  was  the  boiling  point  determined 
and  by  whom?     Another  name? 

19.  What  becomes  of  the  emanations?    What  is  meant  by  "  half  period  "? 

20.  What  are  radioactive  "  deposits  "? 

.     21.  What  is  the  distegration  hypothesis  of  Rutherford  and  Soddy?     What  about 
the  valence  of  a  and  j3  ray  products  and  their  position  in  the  Periodic  System? 

22.  In  the  light  of  21,  what  must  have  been  the  parent  of  radium?     Explain. 
Name  some  other  elements  which  have  descended  in  this  line. 

23.  What  two  series  of  radioactive  elements  are  known? 

24.  How  are  the  atomic  weights  in  the  radioactive  series  calculated?    Check 
two  of  them  in  the  uranium  series. 

25.  What  is  the  direct  parent  of  radium? 

26.  Why  could  radium  not  occur  in  the  thorium  series? 

27.  Name  two  rayless  elements  in  the  above  series.     What  happens  to  them? 

28.  What  happens  when  both  a  and  /3  rays  are  emitted? 

29.  How  are  life  periods  determined?     What  have  they  to  do  with  the  relative 
occurrence  of  the  radioactive  elements?     Illustrate  in  the  case  of  radium  and  uranium. 

30.  Discuss  the  matter  of  "  end-product  "  in  the  radioactive  series. 

31.  Illustrate  the  relation  between  position  of  elements  in  the  Periodic  System 
and  the  kind  of  ray  producing  them. 


CHAPTER  XI 
ATOMIC  STRUCTURE  AND  CHEMICAL  COMBINATION 

General  View  of  Atomic  Structure. — The  facts  which  we  have  cov- 
ered in  our  discussion  of  radiochemistry  and  many  others  which  we  could 
not  include  have  led  to  certain  conclusions  regarding  the  structure  of 
atoms.  Up  to  the  present,  however,  the  matter  has  not  been  very 
thoroughly  worked  out,  although  some  of  the  world's  best  scientists  are 
giving  their  attention  to  it.  We  cannot,  therefore,  go  very  deeply 
into  the  subject,  but  we  may  summarize  the  current  opinions  upon 
which  there  is  a  somewhat  general  agreement,  and  possibly  point  out 
the  lines  along  which  development  is  taking  place.  Perhaps  the  follow- 
ing statements  cover  fairly  well  the  structure  of  the  atom,  as  far  as 
chemists  and  physicists  are  now  agreed  upon  it: 

J  All  atoms  contain  a  positive  nucleus  surrounded  by  a  system  of 
electrons  sufficient  in  number  to  balance  the  nuclear  charge  and  make  the 
atom  neutral. 

In  all  cases  except  that  of  hydrogen,  the  nucleus  contains  both  positive 
charges  and  electrons.  The  single  positive  charge  is  understood  to  be 
equal  to  the  electronic  charge,  but  the  number  of  positive  charges  in  the 
nucleus  is  greater  than  the  number  of  electrons,  leaving  some  free  positive 
charges.  The  number  of  free  positive  charges  in  the  nucleus  is  equal  to 
the  atomic  number  of  the  element.  The  nucleus  is  very  small  compared 
with  the  atom,  but  it  constitutes  nearly  the  whole  mass  of  the  atom. 

The  number  of  electrons  in  the  system  outside  the  nucleus  is  equal  to 
the  number  of  free  charges  in  the  nucleus  and  thus  also  equal  to  the  atomic 
number  of  the  element.  These  electrons  are  arranged  at  comparatively 
great  distances  from  the  nucleus  like  the  planets  in  our  solar  system.  Indeed, 
they  are  often  spoken  of  as  the  "  planetary  system  of  the  element."  The 
chemical  properties  of  the  element,  such  as  valence  and  activity,  depend 
on  the  number  and  arrangement  of  the  planetary  electrons. 

J  The  Nucleus. — J.  J.  Thomson  advanced  the  theory  that  atoms  con- 
sist of  a  system  of  electrons  dispersed  through  a  sphere  of  positive 
electricity.  Rutherford  *  and  his  pupils  showed  that  this  theory  was 
inconsistent  with  the  facts,  however;  for  they  found  that  when  a  par- 

*Phil.  Mag.,  21,  669(1911). 
123 


124        ATOMIC  STRUCTURE  AND  CHEMICAL  COMBINATION 

tides  were  made  to  pass  through  very  thin  pieces  of  metal  foil  some 
of  them  were  scattered  through  a  wide  angle.  They  showed  that  the 
particles  must  pass  directly  through  the  atoms  of  the  metal,  and  proved 
that  the  wide  scattering  or  deflection  could  be  caused  only  by  the  pres- 
ence in  these  atoms  of  an  extremely  concentrated  positive  charge.  This 
led  at  once  to  the  almost  certain  supposition  that  the  positive  part  of 
an  atom  is  contained  in  a  very  small  but  immensely  concentrated 
nucleus.  Their  data  also  enabled  them  to  calculate  the  mass  and  the 
charge  of  the  nucleus.  The  mass  they  found  to  be  practically  the  whole 
mass  of  the  atom;  and  the  charge  was  equal  to  the  electronic  charge 
multiplied  by  about  half  the  atomic  weight  (the  atomic  number)  of  the 
element. 

The  work  of  Moseley  *  on  X-ray  spectra  also  throws  light  on  the 
magnitude  of  the  free  nuclear  charge.  Moseley  found  that  when  X-rays 
were  allowed  to  strike  the  surface  of  an  element  they  were  reflected  off 
in  such  a  way  as  to  form  a  spectrum  which  could  be  photographed. 
Certain  lines  were  always  present.  Two  of  these  which  were  especially 
conspicious  were  named  the  a.  and  the  /j  lines.  The  position  of  these 
lines  depended  on  the  element  used.  In  going  from  one  element  to  the 
next  higher  in  atomic  weight,  the  lines  were  shifted  towards  the  violet. 
From  the  position  of  the  lines  in  any  case  the  frequency  of  the  X-ray 
waves  could  be  calculated.  Between  these  frequencies  of  the  X-ray 
spectra  for  the  different  elements  and  the  atomic  numbers  of  the  ele- 
ments Mosely  found  a  very  simple  relationship.  Thus,  with  the  a  line 
he  found  the  relationship  to  be  expressed  by  the  simple  equation 
v  =  K(N—  I)2,  in  which  v  is  the  frequency,  N  the  atomic  number,  and 
K  a  constant  which  can  be  calculated  once  for  all  by  substituting  the 
atomic  number  of  one  element.  If  13  is  substituted  for  N  in  the  case  of 
aluminum  along  with  the  observed  frequency,  (v),  K  is  obtained. 
If  this  value  for  K  is  then  used  along  with  the  frequency  for  silicon 
the  value  of  N  is  found  to  be  14,  which  is  the  atomic  number  for  silicon. 
After  making  a  large  number  of  observations  and  always  finding  the 
same  relationship  between  frequency  and  atomic  number  Moseley 
became  convinced  that  N  must  represent  the  number  of  free  charges 
on  the  nucleus. 

The  postulate  that  the  nucleus  contains  both  positive  charges  .and 
electrons  seems  to  be  a  necessary  deduction  from  the  facts  of  radio- 
chemistry.  An  atom  shoots  off  an  a  particle  and  is  set  back  two  groups 
in  the  periodic  system.  The  a  particle  carries  with  it  two  positive 

*  Phil.  Mag.,  26,  1024  and  27,  703.  Moseley  was  a  brilliant  young  English 
physicist,  a  Fellow  at  the  University  of  Manchester.  He  was  killed  at  Gallipoli 
in  the  early  part  of  the  war. 


THE  PLANETARY  SYSTEM  125 

charges,  and  so,  to  leave  the  product  neutral,  two  electrons  must  be 
dropped  out  of  the  planetary  system.  These  electrons  are  not  of  high 
speed,  however,  and  so  do  not  appear  as  (3  rays.  When  a  j8  particle  is 
shot  out  of  an  atom  the  atom  is  advanced  one  group  in  the  periodic 
system,  and  thus  becomes  another  kind  of  atom  with  different  proper- 
ties. If  this  |8  particle  came  from  the  planetary  system,  the  nature  of  the 
element  would  not  be  changed;  it  would  merely  become  a  positive  ion, 
and  would  return  to  its  former  state  on  coming  in  contact  with  an 
electron.  It  does  not  do  this,  and  so  it  is  assumed  that  the  /3  particle 
comes  from  the  nucleus. 

The  nature  of  the  elementary  positive  charges  of  which  the  nucleus 
is  mainly  constituted  is  not  definitely  known.  As  we  have  said  before, 
their  magnitude  is  assumed  to  be  the  same  as  that  of  the  electron 
(4.77xlO~10  electrostatic  units).  Rutherford*  suggests  that,  since 
a  particles  are  so  often  emitted  by  the  radioactive  elements,  the  a  par- 
ticle may  be  one  of  the  fundamental  units  of  the  nucleus.  He  suggests 
also  that  the  hydrogen  ion  may  be  one  of  the  fundamental  units.  The 
hydrogen  ion  carries  one  unit  charge  and  the  a  particle  two,  but  the 
mass  of  the  a  particle  is  four  times  that  of  the  hydrogen  ion.  We  are 
inclined  to  think,  therefore,  that  the  a  particle  contains  four  hydrogen 
ions  and  two  electrons.  That  arrangement  would  give  it  the  proper 
mass  of  four,  and  also  account  for  its  double  positive  charge.  This 
statement,  of  course,  commits  us  to  the  supposition  that  the  hydrogen 
ion  is  the  elementary  positive  charge. 

The  Planetary  System. — Several  attempts  have  been  made  to  show 
how  the  electrons  are  arranged  in  the  planetary  systems  of  the  elements 
to  give  them  the  properties  we  know  them  to  possess.  All  of  these  have 
been  more  or  less  successful.  We  shall  outline  one  or  two  only. 

Bohr  f  suggests  that  the  electrons  are  arranged  in  concentric  circles, 
all  in  one  plane,  about  the  nucleus,  and  has  developed  a  rather  elaborate 
theory  on  this  basis.  His  theory  seems  to  succeed,  however,  only  in 
those  cases  where  the  number  of  electrons  is  small.  Also,  the  facts  of 
stereochemistry  prove  almost  beyond  the  shadow  of  a  doubt  that  the 
four  valences  of  the  carbon  atom  extend  out  in  three  dimensions,  and 
Bohr's  theory  could  not  cover  such  an  arrangement  at  all.  Physicists, 
who  do  not  appreciate  the  weight  of  this  evidence,  are  inclined  to  accept 
Bohr's  theory,  but  chemists  hesitate  to  do  so,  although  all  must  admit 
that  the  theory  does  succeed  well  in  many  cases. 

*  Radioactive  Substances  and  their  Radiations,  p.  621.  See  also  paper  by  the 
same  author  on  the  complex  nature  of  the  nitrogen  atom.  Science,  Nov.  21,  1919. 

t  Phil.  Mag.,  26,  476,  857  (1913).  [Niles  Bohr,  Professor  of  Theoretical  Physics, 
University  of  Copenhagen.] 


126        ATOMIC  STRUCTURE  AND  CHEMICAL  COMBINATION 

Another  point  demanded  by  Bohr's  theory  is  that  the  electrons  be 
in  rapid  revolution  around  the  nucleus.  Physicists,  in  general,  seem  to 
think  this  a  necessary  hypothesis  to  account  for  the  fact  that  the 
electrons  do  not  fall  into  the  nucleus.  Chemists,  on  the  other  hand, 
cannot  account  for  the  known  facts  of  chemical  combination  and  valence 
on  this  basis. 

Another  partially  successful  theory  is  the  so-called  "  octet  "  theory 
of  Lewis  *  and  Langmuir.f  The  theory  was  first  presented  by  Lewis, 
but  afterwards  developed  and  very  much  extended  by  Langmuir. 
We  may  begin  the  discussion  of  this  theory  with  the  following  postulates : 

Postulate  1. — The  planetary  electrons  in  a  given  atom  are  distributed 
through  a  series  of  concentric  shells  having  the  nucleus  of  the  atom  at  the 
common  center.  The  shells  are  of  equal  thickness.  The  mean  radii  are, 
therefore,  in  the  proportion  of  1  :  2  :  3  :  4)  ana  the  surface  areas  are  in 
the  proportion  of  1  :  4  •  9  :  16. 

Postulate  2. — Each  shell  is  divided  into  cells,\  or  compartments,  of 
equal  areas.  The  first  shell  contains  2  cells;  the  second  shell,  with  four 
times  the  area,  contains  8  cells;  the  third  contains  18;  and  the  fourth 
contains  32. 

Postulate  3. — Each  cell  in  the  first  shell  may  contain  1  electron  only. 
Each  of  the  other  cells  may  contain  either  1  or  2.  All  the  inner  cells  must 
contain  their  full  quota  before  the  outer  cells  can  contain  any,  and  no  cell 
in  the  outside  layer  can  contain  2  until  all  have  at  least  1. 

The  following  figures  may  help  to  make  the  postulates  clearer: 

•  •  v 

Two  cells:    each  may  contain  1   electron  only.     This  shell  is  understood 

to  be  inside  Shell  II  and  concentric  with  it. 
Shell  I 

FIG.  12. 


Eight  cells:    four  in  sight  and  four   on    the   reverse    side.      After 
Shell  I  is  complete  Shell  II  begins.     It  may  contain  1  electron,  or  2,  or 
3,  up  to  8,  when  the  first  layer  is  complete.     It  may  then  add  1  or  2  or  3 
more  electrons,  up  to  8,  making  16  in  all,  2  in  each  cell.     When  Shell  II         ^^./^^ 
is  complete  the  total  number  of  electrons  in  I  and  II  is  18.  Shell  II 

FIG.  13. 

*  Gilbert  N.  Lewis,  Professor  of  Chemistry,  University  of  California.  Jour. 
Am.  Chem.  Soc.,  38,  762  (1916). 

t  Irving  Langmuir,  Research  Chemist,  General  Electric  Co.,  Schnectady,  N.  Y. 
Jour.  Am.  Chem.  Soc.,  41,  868  (1919). 

J  Langmuir  does  not  mean  by  this  that  the  shell  actually  possesses  substance, 
and  that  this  substance  is  divided  up  into  pockets  or  bins.  He  means  simply  that 
the  electrons  arrange  themselves  in  definite  spherical  layers  and  that  each  electron 
has  a  certain  space,  all  its  own,  from  which  other  electrons  are  excluded. 


THE  PLANETARY  SYSTEM 


127 


Eighteen  cells:  sixteen  in  the  two  zones  and  two  at  the 
poles.  After  Shells  I  and  II  are  completed  Shell  III  begins. 
It  may  have  1,  or  2,  or  3  electrons,  up  to  18,  when  the  first 
layer  is  complete.  It  may  then  add  1  or  2  or  3  more  elec- 
trons, up  to  18  to  complete  the  second  layer,  making  36  in 
all.  When  Shell  III  is  complete  the  total  number  of  elec- 
trons in  I,  II,  and  III  is  54. 


Shell  in 
FIG.  14. 


Thirty- two  cells:  sixteen  in  each  zone.  After  Shells 
I,  II,  and  III  are  complete,  Shell  IV  begins.  It  may 
contain  from  1  to  32  electrons  to  complete  the  first  layer, 
and  may  then  add  1  electron  in  each  cell.  If  the  second 
layer  were  completed  the  shell  would  contain  64  electrons. 
But  the  second  layer  ends  with  uranium,  when  6  cells 
have  the  second  electron.  This  gives  for  all  4  shells  a 
total  of  2  +  16+36+38,  or  92  electrons.  (Note  that  this 
number  is  the  same  as  the  atomic  number  of  uranium.) 


Shell  IV 
FIG.  15. 


The  chart  on  page  128  shows  how  the  electrons  are  distributed 
through  the  shells  in  the  case  of  the  individual  elements. 

Column  2  contains  the  atomic  numbers  of  the  elements.  It  must 
not  be  forgotten,  however,  that  this  number  also  represents  the  number 
of  free  positive  charges  on  the  nucleus,  and  also  the  number  of  electrons 
in  the  planetary  system.  That  the  latter  statement  is  true  can  be 
seen  by  adding  the  electrons  found  in  the  separate  shells. 

Note  how  the  shells  are  filled.  The  first  shell,  which  can  contain 
only  2  electrons,  is  completed  with  helium.  The  second  shell  begins 
with  lithium,  and  the  first  layer  is  completed  with  neon.  The  second 
layer  then  begins  with  sodium,  and  is  completed  with  argon.  The 
third  shell  begins  with  potassium  and  completes  the  first  layer  with 
krypton.  The  second  layer  begins  with  rubidium  and  is  completed 
with  xenon.  The  fourth  shell  begins  with  caesium  and  completes  the 
first  layer  with  niton.  The  second  layer  begins  with  an  alkali  element 
yet  to  be  discovered  (No.  87)  and  is  never  completed. 

The  chart  shows  at  a  glance  the  exact  distribution  of  the  planetary 
electrons  for  any  element.  Take  nickel,  for  example:  This  element 
contains  28  planetary  electrons  in  all.  Of  these,  2  are  in  the  first  shell, 
16  are  in  the  second,  and  10  are  in  the  third. 

Systems  of  great  stability  are  indicated  by  the  heavy  underscoring; 
those  of  more  than  average  stability  by  dotted  underscoring.  Note 
that  the  inert  gases  represent  the  most  stable  systems,  and  the  third 
member  of  the  transition  groups  the  next  in  stability. 


128        ATOMIC  STRUCTURE  AND  CHEMICAL  COMBINATION 


DISTRIBUTION  OF  THE  ELECTRONS  THROUGH  THE  ATOMIC  SHELLS 


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47 
48 
49 
50 
51 
52 
53 
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2 
2 
2 
2 
2 
2 
2 
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8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
-8+8 

18  +  11 

18+12 
18+13 
18+14 
18  +  15 
18  +  16 
18+17 
18+18 

Li 
Be 
B 
C 

N 
0 
F 

Ne 

3 
4 
5 

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8 
9 
10 

2 
2 
2 
2 
2 
2 
2 
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2 
3 
4 
5 

6 

7 
8 

Cs 
Ba 
La 
Ce 
Pr 
Nd 

Sa" 
Eu 
Gd 
Tb 
Dy 
He 
Er 

Tmi 
Tm2 
Yb 
Lu 
Ta 
W 

OB 

Ir 
Pt 

55 
56 
57 
58 
59 
60 
61 
62 
63 
64 
65 
66 
67 
68 

2 
2 
2 

2 

2 

2 
2 
2 

2 
2 
2 
2 
2 
2 

8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 

18  +  18 
18+18 
18  +  18 
18+18 
18  +  18 
18  +  18 
18  +  18 
18  +  18 
18  +  18 
18  +  18 
18+18 
18  +  18 
18  +  18 
18  +  18 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 

Na 
Mg 
Al 
Si 
P 
S 
Cl 
A 

11 
12 
13 
14 
15 
16 
17 
18 

2 
2 

2 
2 
2 
2 
2 
2 

8  +  1 
8+2 
8+3 
8+4 
8+5 
8+6 
8+7 
8+8 

K 

Ca 
Sc 
Ti 
V 
Cr 
Mn 
Fe 
Co 
Ni 

"Cu" 

Zn 
Ga 
Ge 
As 
Se 
Br 
Kr 

19 
20 
21 
22 
23 
24 
25 
26 
27 
28 

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30 
31 
32 
33 
34 
35 
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2 
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2 
2 
2 
2 
2 
2 
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2 
2 
2 
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8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 

's+s' 

8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 

1 

2 
3 

4 
5 
6 

7 
8 
9 
10 

69 
70 
71 

72 
73 
74 
75 
76 
77 
78 

2 
2 
2 
2 
2 
2 
2 
2 
2 
2 

8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 

18+18 
18  +  18 
18  +  18 
18  +  18 
18  +  18 
18  +  18 
18  +  18 
18  +  18 
18  +  18 
18+18 

15 
16 
17 
18 
19 
20 
21 
22 
23 
24 

11 
12 
13 
14 
15 
16 
17 
18 

Au 
Hg 
TI 
Pb 
Bi 
Po 

Ni 

79 
80 

81 
82 
83 
84 
85 
86 

2 
2 
2 
2 
2 
2 
2 
2 

8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 

18+18 
18  +  18 
18  +  18 
18  +  18 
18+18 
18  +  18 
18  +  18 
18+18 

25 
26 
27 
28 
29 
30 
31 
32 

Rb 
Sr 
Y 
Zr 
Cb 
Mo 

Ru 
Rh 
Pd 

37 
38 
39 
40 
41 
42 
43 
44 
45 
46 

2 
2 

2 
2 
2 

2 

2 
2 
2 
2 

8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 
8+8 

18+  1 
18+  2 
18+  3 
18+-  4 
18+  5 
18+  6 
18+  7 
18+  8 
18+  9 
18+10 

Ra 
Ac 
Th 

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87 
88 
89 
90 
91 
92 

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2 
2 
2 
2 
2 
2 

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8+8 
8+8 
8+8 
8+8 
8+8 

18  +  18 
18  +  18 
18  +  18 
18  +  18 
18  +  18 
18+18 

32  +  1 

32+2 
32+3 
32+4 
32+5 
32+6 

CHEMICAL  COMBINATION  AND  PROPERTIES  OF  ELEMENTS    129 

Chemical  Combination  and  the  Properties  of  Elements  and  Com- 
pounds in  the  Light  of  the  Lewis-Langmuir  Theory. — Langmuir's  theory 
covering  properties  and  combinations  may  be  summed  up  as  follows: 

Postulate  4- — The  properties  of  the  elements  depend  on  the  number  and 
arrangement  of  the  electrons  in  the  outside  layer,*  and  on  the  case  with 
which  they  are  able  to  revert  to  more  stable  forms  by  giving  up  or  taking 
on  electrons  or  by  sharing  their  outside  electrons  with  other  atoms. 

The  most  stable  arrangement  of  electrons  is  the  pair,  represented  by  the 
helium  atom.  The  next  most  stable  arrangement  is  the  group  of  8  (the 
octet),  as  seen  in  the  atoms  of  neon  and  argon  and  less  notably  in  the  other 
inert  gases.  Certain  other  forms  are  quite  stable  also;  notably  the  arrange- 
ment seen  in  nickel,  palladium,  and  platinum. 

Postulate  5. — Chemical  combination  results  from  the  effort  made  by  the 
elements  to  form  stable  pairs  or  octets  by  transference  or  sharing  of  electrons. 

A  word  of  explanation  is  necessary  here.  Atoms  may  combine  in 
two  ways:  (1)  An  electron  may  be  transferred  bodily  from  one  atom  to 
another.  When  this  is  done  the  atom  from  which  the  electron  comes 
becomes  positive,  because  one  free  charge  on  the  nucleus  is  now  unbal- 
anced. The  atom  which  takes  up  the  electron  becomes  negative, 
because  it  now  has  one  too  many  electrons  to  balance  its  nuclear  charge. 
The  result  is  a  positive  ion  and  a  negative  ion,  which  are  held  together 
by  electrostatic  attraction.  Sodium  and  chlorine  unite  in  this  way  to 
form  sodium  chloride,  Na+Cl~.  A  compound  thus  formed  is  strongly 
polar;  that  is,  it  has  a  positive  end  and  a  negative  end,  like  a  magnet, 
and  if  the  compound  is  electrolyzed  the  two  parts  are  attracted  to 
opposite  poles.  A  strongly  polar  compound  does  not  usually  exist  in 
individual  molecules,  but  tends  to  build  itself  into  aggregates  or  into  the 
lattice  structure  characteristic  of  crystalline  solids.  (2)  A  pair  of 
electrons  may  be  held  in  common,  or  shared,  by  2  atoms.  Suppose 
2  partial  octets  each  lack  1  electron,  as  indicated  thus: 


FIG.  16. — The  Sharing  Process. 
By  bringing  the  2  atoms  together  the  deficiency  in  each  octet  is 

*  The  electrons  in  the  outside  layer  are  usually  called  "valence  electrons": 
Lewis  calls  the  rest  of  the  atom  its  "  kernel." 


130        ATOMIC  STRUCTURE  AND  CHEMICAL  COMBINATION 

satisfied  by  an  electron  from  the  other  octet,  as  indicated  by  the  arrows. 
We  then  have  the  2  octets  joined  through  the  common  pair,  thus: 


FIG.  17. — A  Molecule  Formed  by  the  Sharing  Process. 

Note  that  there  was  no  transference  of  electrons  here,  and  so  each 
atom  is  as  neutral  as  it  was  before.  The  compound  is,  therefore, 
non-polar.  Non-polar  compounds  exist  as  individual  molecules. 
Organic  compounds  are  very  largely  of  this  type.  It  is  among  them 
also  that  our  molecular  weight  methods  are  successful. 

The  pair  of  electrons  held  in  common  between  2  octets  represents 
what  we  call  a  "  single  bond  "  in  organic  chemistry.  Two  pairs  held  in 
common  would  represent  a  "  double  bond." 

Langmuir  has  developed  a  fundamental  equation  covering  this 
octet  theory  of  valence,  which  has  a  very  useful  application  in  determin- 
ing the  structure  of  non-polar  compounds.  We  can  best  give  this  here 
before  we  go  on  to  the  applications  of  the  theory.  A  complete  octet 
has  8  electrons  placed  at  the  8  corners  of  a  cube.  Two  separate  octets 
therefore  require  16  electrons.  But  when  2  octets  share  1  pair  of  elec- 
trons only  14  are  required  to  complete  the  2  octets,  as  can  be  seen  from 
the  sketches  above.  It  is  evident,  therefore,  that  whenever  2  octets 
share  a  pair  of  electrons,  2  less  electrons  are  needed  to  complete  the  2 
octets.  In  any  molecule,  therefore,  the  total  number  of  electrons  in  the 
outer  layers  of  all  the  atoms  will  be  8  times  the  number  of  octets  pro- 
duced, minus  twice  the  number  of  pairs  held  in  common  between  octets. 
This  may  be  stated  thus: 

e  =  Sn-2P 

where  e  is  the  total  number  of  electrons  available  for  forming  octets, 
n  is  the  number  of  octets  produced,  and  P  is  the  number  of  pairs  held 
in  common  by  octets.  In  working  out  the  structure  of  a  compound 
we  usually  want  to  know  how  many  pairs  are  held  in  common  between 
octets,  Hence,  our  equation  is  best  stated  in  the  form 


P= 


Sn-e 


CHEMICAL  COMBINATION  AND  PROPERTIES  OF  ELEMENTS    131 

Valence  determined  by  this  method,  counting  each  common  pair  as  a 
single  bond,  will  not  always  be  found  to  correspond  with  our  old  theory 
of  valence.  We  shall  see  this  in  the  examples  presented. 

We  shall  now  proceed  to  give  a  few  examples  showing  the  application 
of  the  theory  in  the  matter  of  properties  and  combination. 

Helium  contains  a  positive  nucleus  with  2  free  charges,  and  outside 
this  is  a  planetary  system  consisting  of  2  electrons,  completing  the  first 
shell.  Here  we  have  the  most  stable  arrangement  possible,  the  "  stable 
pair  "  of  Postulate  4.  This  makes  the  helium  atom  perfectly  satisfied 
with  its  own  condition;  it  has  no  tendency  to  gain  or  lose  electrons,  and 
so  is  almost  absolutely  inert.  For  this  reason  helium  forms  no  com- 
pounds, and  the  atoms  do  not  tend  to  combine  into  molecules  or  take 
on  the  liquid  form.  The  latter  statement  is  proved  by  the  fact  that 
helium  is  found  to  be  monatomic  and  that  it  is  the  most  difficult  of  all 
the  gases  to  liquefy. 


The  helium  atom  may  be  represented  thus : 


FIG.  18. — The  Helium  Atom. 

It  is  understood,  of  course,  that  the  nucleus,  represented  by  the  black 
dot,  is  at  the  center  of  the  sphere,  and  that  the  2  electrons  are  on  the 
axis,  1  in  each  "  cell." 

The  hydrogen  atom  is  made  up  of  a  positive  nucleus  with  1  charge 
and  a  planetary  system  of  1  lone  electron.  This  is  a  very  unsymmetrical 
arrangement,  and  therefore  the  tendency  is  for  2  atoms  to  unite  into  a 
molecule  and  thus  form  a  stable  pair.  To  accomplish  this  the  2  nuclei 
come  together  at  a  center  and  then  the  2  electrons  arrange  themselves 
as  in  the  helium  atom.  This  makes  an  arrangement  second  in  stability 
only  to  that  of  the  helium  atom.  As  we  should  expect,  therefore, 
molecular  hydrogen  is  rather  inactive  and  is  very  difficult  to  liquefy. 
Atomic  hydrogen  should  be  very  active. 

Lithium,  atomic  number  3,  has  3  free  positive  charges  on  the  nucleus 
and  3  electrons  outside.  Two  of  these  electrons  form  a  stable  pair, 
completing  the  first  shell.  The  third  electron  occupies  one  of  the  cells 
in  the  second  shell.  The  tendency  is  for  the  atom  to  get  rid  of  this  1 
electron  and  thus  revert  to  the  form  of  the  helium  atom,  that  is,  the 
stable  pair.  It  cannot  do  -this  except  when  some  other  atom  is  near 
which  needs  an  extra  electron.  When  it  does  give  up  this  electron  it 
leaves  1  positive  charge  on  the  nucleus  unbalanced,  and  this  changes 
the  lithium  atom  into  a  univalent  lithium  ion  (Li+).  The  structure  of 


132        ATOMIC  STRUCTURE  AND  CHEMICAL  COMBINATION 


the  atom,  with  its  positive  kernel  and  its  single  electron  at  one  side, 
is  that  of  an  electrical  doublet.  In  other  words  the  lithium  atom  is 
strongly  polar.  It  therefore  attracts  other  lithium  atoms,  a  second  on 
the  first,  a  third  on  the  second,  and  so  on,  building  thus  the  lattice  struc- 
ture of  a  crystalline  solid.  Since  the  electrons  are  only  weakly  held  they 
are  easily  made  to  shift  along  from  atom  to  atom  when  an  electrical 
potential  is  applied.  In  other  words,  the  solid  lithium  is  a  metal  which 
conducts  the  electric  current. 

Carbon,  atomic  number  6,  has  6  positive  charges  on  the  nucleus  and 
6  electrons.  Two  of  the  latter  form  a  pair  next  the  nucleus,  and  the 
other  4  occupy  4  of  the  8  cells  in  the  second  shell. 

There  are  two  possibilities  here;  the  atom  may  drop  4  electrons 
and  revert  to  the  form  of  helium  or  it  may  take  on  4  more  and  thus 
complete  its  octet.  This  gives  us  at  once  the  key  to  Abegg's  rule  that 
the  sum  of  the  maximum  positive  and  negative  valences  of  an  element  is 
8.  If  the  atom  gives  up  4  electrons  its  valence  becomes  +4;  if  it  takes 
up  4  electrons  its  valence  is  —4. 

Carbon  unites  with  hydrogen  to  form  methane,  CH4.  In  this  case 
the  4  hydrogen  atoms  supply  the  4  extra  electrons.  Hydrogen,  however, 
is  not  anxious  to  part  with  its  electron,  so  it  simply  shares  it  with 
the  carbon  atom  and  forms  a  stable  pair  with  another  electron  in  the 
octet.  At  the  same  time  the  carbon  atom  completes  its  octet.  If  we 
represent  the  incomplete  octet  of  the  carbon  atom  and  4  hydrogen  atoms 
thus,  we  see  how  the  latter  may  attach  themselves  to  complete  the 
octet.  As  this  is  accomplished  the  hydrogen  nucleus  is  attracted  by 
the  neighboring  electron  in  the  octet  as  well  as  by  its  own  electron, 
thus  forming  a  stable  pair.  The  next  figure  shows  how  affairs  stand 
after  the  sharing  process  is  accomplished. 


o 


FIG.  19. — Atoms  of  Hydrogen  about  to 
Combine  with  an  Atom  of  Carbon. 


FIG.  20. — A  Molecule  of  Methane 
Formed  as  in  Fig.  19. 


Methane  is  a  non-polar  compound,  no  electrons  being  transferred. 
It  may  be  remarked  in  passing  that  the  4  electrons  in  the  partial 
octet  are  probably  actually  arranged  as  indicated  in  the  first  figure. 


CHEMICAL  COMBINATION  AND  PROPERTIES  OF  ELEMENTS    133 

They  would  surely  repel  each  other,  and  thus  get  as  far  apart  as  possible. 
This  would  place  them  so  that  the  distance  between  any  2  was  a  diagonal 
of  the  cube  face,  as  seen  above.  After  the  combination  with  hydrogen, 
as  seen  in  the  second  figure,  the  hydrogen  nuclei  would  tend  to  draw 
their  pairs  of  electrons  together.  Those  to  the  left  would  thus  be 
drawn  together  vertically,  those  to  the  right  horizontally,  The  result 
would  be  a  regular  tetrahedron.  We  thus 
have  the  tetrahedral  carbon  atom,  which  is 
one  of  the  fundamental  concepts  of  organic 
chemistry. 

The  oxygen  atom  contains  8  electrons  alto- 
gether; 6  of  these  are  in  the  second  shell. 
It  thus  needs  2  more  to  complete  its  octet. 
When  oxygen  atoms  unite  with  each  other  to 
form  molecules,  62,  they  complete  their  octets 
by  sharing  electrons.  By  using  our  funda- 
mental equation  developed  above,  we  can  tell 
how  many  pairs  of  electrons  are  thus  shared, 

and  are  thus  able  to  determine  the  structure  of  the  oxygen  molecule. 
The  equation  was  given  as 


FIG.  21 —The  Tetrahedral 
Carbon  Atom. 


In  the  case  above,  n  =  2  and  e  =  12.     Thereiore 

p=16-12 


or  2,  which  means  that  2  pairs  of  electrons  are  held  in  common  by  the 
2  octets.  In  other  words,  each  octet  places  2  of  its  electrons  at  the 
disposal  of  the  other  octet,  both  being  thus  made  complete.  The 
oxygen  molecule  may,  therefore,  be  represented  thus; 


7 

r 

....  ^ 
> 

7  — 
—  C 

S 

i 

j 
—C 

FIG.  22. — A  Molecule  of  Oxygen. 

It  should  be  noted  that  the  octet  theory  of  valence  here  corresponds 
with  the  old  theory,  if  we  regard  each  pair  of  electrons  shared  as  corre- 
sponding to  a  single  valence  bond.  It  differs,  however,  in  one  way: 


134         ATOMIC  STRUCTURE  AND  CHEMICAL  COMBINATION 


it  does  not  require  us  to  make  one  atom  positive  and  the  other  negative. 
Oxygen  is  non-polar,  as  the  new  theory  leads  us  to  expect.  It  is,  of 
course,  quite  possible  that  if  oxygen  gas  were  dissociated  into  atoms 
at  very  high  temperature  the  2  octets  might  not  both  get  back  the 
electrons  they  have  shared;  one  might  retain  2  extra  electrons,  thus 
becoming  negative  and  leaving  the  other  positive.  Possibly  the  iodine 
molecule  also  does  this  at  high  temperatures  (see  page  76). 

0?one,  Os,  evidently  contains  3  octets.     Let  us  see  what  structure 
our  theory  would  indicate.     In  this  case  n  =  3,  e  =  18.     Therefore, 


P  = 


24-18 


or  3,  which  means  3  pairs  of  electrons  are  shared  among  the  3  octets. 
The  only  way  in  which  this  can  be  done  is  for  2  octets  to  share  2  pairs, 
as  in  62,  and  for  one  of  these  to  share  another  pair  with  the  third  atom. 
The  sketch  indicates  the  structure: 


Q 


FIG.  23.— A  Molecule  of  Ozone. 


This  formula  seems  to  indicate  that  the  third  atom  is  less  firmly 
attached,  and  may  thus  account  for  the  instability  of  ozone.  Note 
that  this  atom  is  attached  by  a  single  bond  (one  common  pair). 

Fluorine,  the  last  member  of  the  first  period,  has  7  electrons  in  its 
outer  shell,  and  its  properties  are  determined  mainly  by  the  tremendous 
energy  with  which  it  strives  to  complete  its  octet.  Fluorine  is  the 
most  active  of  all  the  elements,  and  this  activity  is  undoubtedly  due  to 
this  cause. 

We  have  seen  that  lithium  has  a  lone  electron  in  its  second  shell, 
of  which  it  would  be  glad  to  be  rid.  What  would  happen  if  lithium  and 
fluorine  came  together  is,  therefore,  perfectly  evident.  The  fluorine 
atom  would  instantly  capture  this  electron,  and  thus  complete  its  octet. 
This  would,  of  course,  leave  the  lithium  kernel  with  an  extra  positive 
charge  as  lithium  ion  (Li+),  and  would  give  the  fluorine  a  negative 


CHEMICAL  COMBINATION  AND  PROPERTIES  OF  ELEMENTS   135 

charge,  as  fluorine  ion  (F~).  Note  that  in  this  case  there  is  an  actual 
transference  of  the  electron.  The  two  ions  are  held  together  by  electro- 
static attraction.  The  compound  is  polar,  of  course,  and  therefore 
builds  itself  into  the  lattice  structure  of  the  crystalline  solid.  If 
melted,  so  that  the  ions  are  free  to  move  about,  it  conducts  the  electric 
current. 

The  next  element  beyond  fluorine  is  neon,  another  of  the  inert  gases. 
In  this  element  \ve  have  again  a  most  stable  configuration.  At  the 
center  of  the  atom  is  a  nucleus  containing  10  positive  charges ;  outside 
this,  is  the  stable  pair  of  electrons  making  up  the  first  shell.  In  the 
second  shell  are  8  more  electrons  placed  at  the  corners  of  a  cube  and 
thus  completing  an  octet.  Nothing  could  be  more  stable  than  this, 
except  the  stable  pair  above.  Indeed,  this  is  the  stable  form  towards 
which  the  elements  in  the  latter  part  of  the  first  period  have  been 
striving.  As  we  should  expect,  therefore,  neon  has  no  tendency  to 
take  on  or  give  off  electrons,  and  so  forms  no  compounds.  Being  so 
symmetrical  also,  it  has  practically  no  external  field  tending  to  cause 
the  formation  of  molecules.  It  is  therefore  a  monatomic  gas,  very 
difficult  to  liquefy.  Since  the  outside  electrons  are  farther  from  the 
nucleus  than  in  the  case  of  helium,  it  is  a  little  less  stable  and  inert  than 
that  gas,  as  we  should  expect. 

Beyond  neon  we  have  practically  the  same  things  repeated  as  in  the 
first  period.  Sodium  has  one  more  charge  on  the  nucleus  than  neon,  and 
so  must  have  one  more  electron  outside.  This  electron  goes  into  the 
second  shell,  as  have  those  of  the  first  period,  but  it  stands  in  the  second 
layer  of  this  shell.  Note,  however,  that  it  stands  alone  as  the  only 
member  of  this  second  layer,  and  thus  gives  sodium  exactly  the  same 
kind  of  dissymmetry  as  that  possessed  by  lithium.  Its  properties  are, 
therefore,  very  much  like  those  of  lithium,  except  that  it  has  even 
greater  tendency  to  part  with  its  lone  electron  because  this  electron 
is  farther  from  the  nucleus  and  thus  less  attracted  by  it. 

We  hardly  need  mention  the  other  members  of  the  period.  Their 
properties  correspond  very  closely  with  those  of  the  first  period  because 
the  configuration  is  the  same. 

Just  a  word  about  the  first  long  period:  Argon,  the  first  member, 
contains  8  electrons  in  each  layer  of  its  second  shell,  standing,  therefore, 
as  the  stable  form  towards  which  the  elements  before  it  have  been 
striving.  It  is  monatomic  and  inert,  of  course,  but  not  quite  so  inert 
as  neon,  because  of  its  larger  volume.  Beyond  argon  we  have  potassium, 
with  a  lone  electron  in  the  third  shell,  and  therefore  like  lithium  and 
sodium ;  and  beyond  this  matters  proceed  at  first  as  in  the  other  periods. 
But  this  is  a  long  period;  there  will  be  18  electrons  in  the  first  layer. 


136        ATOMIC  STRUCTURE  AND  CHEMICAL  COMBINATION 

At  first  the  elements  strive  to  revert  to  the  form  of  argon;  but  later  this 
tendency  becomes  weak,  and  another  type  stands  out.  This  is  nickel. 
We  must  not  stop  for  Langmuir's  explanation  of  this;  but  the  chart 
shows  that  nickel  has  10  electrons  in  its  outer  layer,  4  in  each  zone 
and  1  at  each  pole.  This  makes  a  very  symmetrical  arrangement  pos- 
sible, and  probably  accounts  for  the  stability.  Elements  on  either  side 
of  nickel  tend  to  revert  to  its  form,  and  otherwise  show  points  of 
likeness.  Copper,  an  example,  is  much  more  like  nickel  than  like  the 
alkalies. 

The  second  long  period  fills  up  the  second  layer  of  the  third  shell, 
with  a  stopping  place  at  palladium. 

The  fourth  shell  includes  the  rare  earths,  which  fit  into  the  scheme 
perfectly,  and  need  no  such  special  treatment  as  is  necessary  in  the 
Periodic  System. 

We  can  mention  just  two  more  things  before  leaving  Langmuir's 
theory:  one  is  the  structure  of  the  nitrogen  molecule,  and  the  other  is 
what  Langmuir  calls  isosterism. 

The  nitrogen  atom  contains  7  electrons,  and  5  of  these  are  in  the 
second  shell.  Three  more  are  needed  to  complete  the  octet.  The 
molecule  of  nitrogen  is  N2.  If  these  2  atoms  united  by  sharing  electrons, 
each  atom  would  have  to  loan  3  electrons  to  the  other,  making  thus  3 
pairs  of  electrons  shared,  and  presenting  a  triple  linkage,  such  as  is 
seen  in  acetylene  (HC  =  CH) .  Triple  linkages  are  usually  accompanied 
by  great  instability  and  the  easy  formation  of  addition  products. 
Nitrogen  is  very  stable  and  almost  as  inert  as  the  rare  gases.  Langmuir 
thinks,  therefore,  that  the  structure  of  the  nitrogen  molecule  must  be 
like  that  of  the  inert  gases,  and  suggests  that  the  molecule  is  formed 
by  the  merging  of  2  atoms  into  1  octet.  He  thinks  that  the  2  nuclei, 
bearing  their  pairs  of  electrons,  come  together,  and  that  8  of  the  other 
10  electrons  then  form  an  octet  around  this  double  nucleus,  while  the 
last  2  electrons  are  imprisoned  inside.  The  following  sketch  shows 
the  structure;  * 


FIG.  24. — The  Nitrogen  Molecule. 


OTHER  THEORIES  OF  ATOMIC  STRUCTURE 


137 


Langmuir  calls  compounds  isosteric  when  the  molecules  contain  the 
same  total  number  of  electrons  and  have  the  same  configuration. 
When  he  came  to  work  out  the  structure  of  different  compounds  by  use 
of  his  theory,  he  found  that  certain  cases  seemed  to  show  an  identical 
configuration  and  number  of  electrons,  and  reasoned  that  these  sub- 
stances should  have  identical  properties.  Upon  looking  the  matter  up 
he  found  his  theory  confirmed  to  a  remarkable  degree.  Take  the 
gases  nitrogen  and  carbon  monoxide:  The  structure  of  the  nitrogen 
molecules  we  have  just  given  above.  The  structure  of  carbon  monoxide 
is  probably  nearly  identical.  Thus,  the  carbon  atom  has  a  total  of  6 
electrons  and  the  oxygen  atom  has  8,  making  altogether  14,  the  same 
number  as  in  N2.  The  2  nuclei  and  the  14  electrons  are  no  doubt 
arranged  in  the  same  way  also.  The  only  difference  between  the  two 
molecules  is  the  fact  that  the  CO  double  nucleus  is  not  symmetrical, 
having  6+8  charges,  while  that  of  the  nitrogen  is  symmetrical,  having 
7+7  charges.  This  may  account  for  the  somewhat  lesser  stability  of 
the  former.  The  following  table  shows  how  nearly  identical  the  proper- 
ties of  these  two  gases  are : 


CO 

N2 

Freezing  point  (absolute)  

66° 

63° 

Boiling  point  (absolute)  

83° 

78° 

Critical  temperature  (absolute)  
Critical  pressure  (atmospheres)  
Solubility  in  water  (per  cent)  
Density  of  liquid  

122° 
35 
3.5 
0.793 

127° 
33 

2.4 
0.796 

Viscosity  

163 

166 

Carbon  dioxide,  C02,  and  nitrous  oxide,  N20,  are  another  pair  of 
isosteres. 

The  discovery  of  isosterism  is  one  of  the  greatest  triumphs  of  Lang- 
muir's  theory,  for  without  this  theory  no  one  would  have  suspected  that 
isosterism  existed. 

We  must  not  go  farther  with  Langmuir's  interesting  theory.  It 
explains  many  things,  which  we  have  not  space  even  to  mention,  but  we 
have  given  enough  to  show  something  of  its  scope  and  usefulness.  Further 
research  may  show  that  parts  of  the  theory  are  wrong;  but  even  a 
wrong  theory  has  a  distinct  and  high  value  if  it  tends  to  clarify  our 
thinking  and  to  stimulate  further  search  after  the  truth. 

Other  Theories  of  Atomic  Structure. — The  scope  of  this  text  will  not 
permit  us  to  give  details  of  other  theories,  but  we  may  refer  to  a  series 


138        ATOMIC  STRUCTURE  AND  CHEMICAL  COMBINATION 

of  five  valuable  papers  by  Harkins,  which  not  only  present  much  valuable 
new  material,  but  also  furnish  a  splendid  bibliography  on  the  subject. 
These  papers  are  as  follows : 

1.  Changes  of  Mass  and  Weight  Involved  in  the  Formation  of  Complex  Atoms: 
Jour.  Am.  Chem.  Soc.,  37,  1367. 

2.  The  Structure  of  Complex  Atoms.     The  Hydrogen-Helium  System:    Jour. 
Am.  Chem.  Soc.,  37,  1383. 

3.  Recent  Work  on  the  Structure  of  the  Atom:    Jour.  Am.  Chem.  Soc.,  37,  1396. 
This  paper  contains  an  especially  valuable  bibliography,  and  also  a  very  clear  chrono- 
logical arrangement  and  discussion  of  material. 

4.  Energy  Relations  Involved  in  the  Formation  of  Complex  Atoms:  Phil.  Mag., 
30,  723. 

5.  The  Periodic  System  and  the  Properties  of  the  Elements:    Jour.  Am.  Chem. 
Soc.,  38,  169. 

The  Electronic  Conception  of  Valence. — In  dealing  with  the  theories 
of  atomic  structure  and  chemical  combination  we  have  here  and  there 
hinted  at  the  idea  of  valence,  but  have  nowhere  discussed  the  matter  in 
detail.  It  may,  therefore,  be  well  to  bring  together  at  this  point  what 
we  wish  to  say  on  that  subject. 

In  speaking  of  possible  methods  of  combination  we  have  shown  that 
polar  compounds  are  undoubtedly  formed  by  the  transference  of  electrons 
from  one  element  to  another.  We  have  noted  also  that  where  one  elec- 
tron was  transferred  univalent  ions  were  produced.  Valence  in  such 
cases,  therefore,  means  nothing  more  than  the  capacity  an  element 
possesses  to  take  on  or  give  off  electrons.  The  sign  of  the  valence,  too, 
undoubtedly  depends  on  whether  the  electrons  are  taken  on  or  given  off. 
Thus,  an  atom  of  sodium  gives  up  one  electron  and  an  atom  of  chlorine 
takes  it  on,  and  the  two  atoms  are  then  held  together  by  electrostatic 
attraction  to  form  a  "  molecule  "  of  sodium  chloride.  In  so  doing 
sodium  becomes  univalent  positive  and  chlorine  univalent  negative. 
Note  just  why  this  is  so:  The  neutral  sodium  atom  contains  11  free 
positive  charges  in  its  nucleus  balanced  by  11  planetary  electrons 
(see  p.  128).  When  the  atom  gives  up  an  electron  1  nuclear  charge  is 
left  unbalanced,  and  we  have  the  ion  Na+.  Likewise  the  neutral 
chlorine  atom  contains  17  positive  charges  on  the  nucleus  balanced  by 
17  planetary  electrons.  When  the  atom  takes  on  1  extra  electron  we 
have  a  preponderance  of  1  negative  charge,  giving  the  ion  Cl~.  Sodium 
can  give  off  1  electron  only  because  this  1  electron  stands  alone  in  the 
outer  layer  and  the  atom  seeks  to  revert  to  the  more  stable  form  of 
neon.  Chlorine  can  take  on  1  electron  only  because  it  has  7  in  its  outer 
layer  and  thus  needs  just  1  more  to  complete  its  octet.  This  is  why, 
in  combining,  sodium  becomes  univalent  positive  and  chlorine  univalent 


THE  ELECTRONIC  CONCEPTION  OF  VALENCE  139 

negative.  For  similar  reasons  calcium,  in  going  into  combination, 
becomes  bivalent  positive  and  sulphur  bivalent  negative.  (Work  these 
out  from  the  table  as  above.) 

Where  electrons  are  only  shared,  the  valence  capacity  is  not  so  clear. 
We  have  shown,  for  example,  that  the  sharing  of  one  pair  of  electrons 
should  correspond  to  a  single  bond  (univalent),  but  we  have  also  shown 
that  in  the  case  of  ozone  one  of  the  atoms  of  oxygen  concerned  seems  to 
be  trivalent  and  another  univalent  (p.  134).  This  conception  is  some- 
what of  a  shock  to  our  old  idea  of  valence,  for  it  not  only  disturbs  the 
fixed  number  (2)  which  we  have  assigned  to  the  valence  of  oxygen,  but 
it  does  away  with  the  assumption  that  the  valence  should  be  negative. 
In  such  a  compound  as  chloroform  (CHCls)  our  former  theory  made 
carbon  negative  with  respect  to  hydrogen  and  positive  with  respect  to 
chlorine  (p.  77).  As  chloroform  is  a  non-polar  compound;  however, 
the  new  theory  would  hold  that  the  electrons  are  only  shared  in  any 
case,  and  so  the  hypothesis  of  positive  and  negative  valence  is  not 
needed. 

In  view  of  certain  facts  which  we  shall  discuss  later  *  it  does  not 
seem  improbable  that  both  polar  and  non-polar  combination  may  occur 
in  the  same  compound.  Thus,  some  of  the  molecules  of  EkS  may  be 
polar  and  some  of  them  non-polar,  and  in  H2SO4  the  combination 
between  H  and  0  may  be  polar  while  that  between  S  and  0  may  be 
non-polar. 

Oxidation  and  reduction  reactions  are  best  explained  as  transference 
(polar)  combinations.  Thus,  when  ferrous  iron  is  oxidized  by  bromine, 
according  to  the  reaction 


an  electron  is  undoubtedly  transferred  from  the  iron  atom  to  the  bromine 
atom.  The  nucleus  of  the  neutral  iron  atom  has  in  it  26  free  positive 
charges  (p.  128)  balanced  by  a  planetary  system  of  26  electrons.  In 
the  ferrous  ion  the  planetary  system  has  only  24  electrons,  leaving  2 
of  the  nuclear  charges  unbalanced,  as  represented  in  Fe++.  In  the 
process  of  oxidation  another  electron  is  captured  by  the  bromine  atom. 
leaving  3  nuclear  charges  unbalanced  as  represented  in  Fe+  +  +  .  The 
neutral  bromine  atom  takes  on  the  extra  electron  to  complete  its  octet, 
but  the  atom  is  thus  given  a  preponderance  of  one  negative  charge  and 
so  becomes  Br~. 

In  terms  of  the  electron  theory  we  should  say,  then,  that  the  act  of 
being  oxidized  meant  the  giving  up  of  electrons  and  the  act  of  being 

*  See  topic,  "  Why  Substances  Do  or  Do  Not  Ionize,"  p.  171. 


140        ATOMIC  STRUCTURE  AND  CHEMICAL  COMBINATION 

reduced  meant  the  taking  on  of  electrons.     It  is  probable  that  all  oxi- 
dation-reduction reactions  can  be  explained  on  this  basis. 


EXERCISES 

1.  What  is  the  general  structure  of  atoms,  as  now  generally  agreed  upon? 

2.  Give  general  description  of  the  "  nucleus  "  and  of  the  "  planetary  system." 

3.  Give  the  points  of  difference  between  J.  J.  Thomson's  and  Rutherford's  theories 
of  the  atom. 

4.  What  was  Moseley's  contribution  regarding  the  nuclear  charge.     Develop 
the  equation  v=K(N—l)2. 

6.  Present  evidence  in  support  of  the  postulate  that  the  nucleus  contains  both 
positive  and  negative  charges. 

6.  What  is  the  nature  of  the  elementary  positive  charge?     What  is  its  magnitude? 

7.  What  is  Bohr's  theory  regarding  the  arrangement  of  the  planetary  electrons? 

8.  Present  three  postulates  covering  the  arrangement  of  the  planetary  electrons 
according  to  the  Lewis-Langmuir  theory. 

9.  Sketch  the  arrangement  of  cells  in  the  four  atomic  shells,  and  show  how  the 
electrons  may  be  distributed  through  them. 

10.  Refer  to  the  table  showing  the  distribution  of  the  electrons  in  the  atomic 
shells  according  to  Langmuir's  theory,  and  present  the  following  details : 

(a)  atomic  number; 

(6)  order  in  which  the  shells  are  filled; 

(c)  arrangement  of  electrons  in  a  few  typical  examples; 

(d)  systems  of  great  stability. 

11.  Give  postulates  4  and  5,   covering  the  matter  of  properties  and  chemical 
combinations. 

12.  What  are  the  two  most  stable  arrangements? 

13.  Give  details  of  the  two  types  of  combination,  one  involving  transference, 
and  the  other  sharing,  of  electrons. 

14.  What  is  meant  by  "  polar  "  and  "  non-polar  "  compounds? 

15.  How  are  single  and  double  bonds  represented  in  the  Langmuir  theory? 

16.  Develop  Langmuir's  formula  covering  the  octet  theory  of  valence. 

17.  Give  the  structure  and  properties  of  helium,  hydrogen,  and  lithium. 

18.  Give  structure  of  the  carbon  atom,  formation  and  properties  of  methane, 
and  then  discuss  the  tetrahedral  nature  of  the  carbon  atom. 

19.  Apply  Langmuir's  equation  to  show  the  structure  of  molecular  oxygen  and 
ozone. 

20.  Discuss  the  combination  of  fluorine  and  lithium,  and  the  properties  of  the 
product. 

21.  Discuss  the  first  long  period. 

22.  Give  structure  of  the  nitrogen  molecule. 

23.  Give  and  explain  one  example  of  isosterism. 

24.  Give  a  summary  of  the  electronic  conception  of  valence,  touching  polar  and 
non-polar  combination  and  oxidation-reduction  reactions. 


CHAPTER  XII 
SOLUBILITY  AND    SUPERSATURATION :    CONCENTRATION 

The  Mechanism  of  Solution  and  the  State  of  Saturation. — When  a 
solid  like  sodium  chloride  is  placed  in  contact  with  a  solvent  like  water, 
the  particles  of  the  solid  fly  off  and  diffuse  about  very  much  after  the 
manner  of  a  gas.  In  this  process  there  are  two  forces  at  work:  first, 
the  kinetic  energy  of  the  molecules,  which  would  tend  to  cause  them  to 
leave  the  solid  just  as  the  molecules  of  a  liquid  fly  off  into  the  space 
above  it ;  second,  the  attraction  of  the  solvent  molecules  for  those  of  the 
solid  (the  solute) .  The  latter  is  probably  the  more  important  factor, 
for  we  know  of  very  few  cases  where  a  solid  "  evaporates  "  without  the 
help  of  the  solvent. 

As  the  molecules,  thus  thrown  into  solution,  dart  about,  some  of 
them  are  certain  to  return  to  the  surface  of  the  solid  and  be  caught 
there;  and  as  the  number  of  molecules  in  solution  increases  the  number 
so  caught  will  also  increase,  until  finally  a  condition  will  be  reached 
where  the  number  of  molecules  returning  to  the  solid  will  equal  the 
number  going  into  solution.  The  state  of  equilibrium  then  existing  is 
called  "  saturation,"  and  a  solution  in  this  state  is  called  a  "  saturated 
solution." 

It  should  be  understood  that  in  a  saturated  solution  in  contact  with 
the  solid  the  tendency  for  the  solid  to  dissolve  and  the  tendency  for 
the  dissolved  molecules  to  return  to  the  solid  are  still  in  full  operation. 
This  can  be  proved  by  taking  a  crystal  of  some  salt  from  which  a  corner 
has  been  filed  off  and  suspending  it  in  its  saturated  solution.  The 
crystal  will  be  mended  without  change  of  weight,  and  there  is  only  one 
way  in  which  this  can  be  accomplished:  a  certain  number  of  molecules 
must  leave  the  perfect  faces  and  a  like  number  must  be  built  on  the 
imperfect  corner.  This  means  a  movement  of  molecules  to  and  from 
the  solid  in  a  saturated  solution. 

When  a  state  of  equilibrium  between  solid  and  solution  has  been 
reached,  the  amount  of  solid  left  over  or  added  has  no  effect.  If  the 
solid  presents  1  sq.  cm.  of  surface  from  which  molecules  can  enter  the 
solution,  the  solution  also  presents  1  sq.  cm.  of  surface  to  the  solid 
from  which  molecules  can  return.  Increasing  the  surface  presented  by 

141 


142      SOLUBILITY  AND  SUPERSATURATION :   CONCENTRATION 

the  solid,  that  is,  increasing  the  amount  of  the  solid,  causes  a  like  increase 
in  the  opposing  surface,  and  the  same  state  of  equilibrium  still  holds. 

Solubility. — Solubility  is  related  to  saturation  very  much  as  vapor 
pressure  is  related  to  saturated  vapor.  Vapor  pressure  is  the  concen- 
centration  of  a  vapor  at  the  point  of  saturation;  solubility  is  the  con- 
centration of  a  solution  at  the  point  of  saturation. 

Solubility  may  be  stated  in  several  different  ways.  Of  these  the 
most  important  are  the  following: 

(1)  Grams  per  100  gm.  of  solvent. 

(2)  Grams  per  100  gm.  of  solution  (percentage  solubility). 

(3)  Moles  per  liter  of  solution  (molar  solubility). 

It  should  be  noted  that  either  one  of  the  first  two  methods  can  be 
calculated  from  the  other,  but  that  method  (3)  cannot  be  so  calculated 
unless  we  have  given  us  also  the  density  of  the  solution.  Suppose,  for 
example,  we  know  that  100  gm.  of  water  dissolve  30  gm.  of  a  salt.  We 
then  calculate  that  the  solution  made  up  of  these  amounts  of  water  and 
salt  would  weigh  130  gm.  In  other  words,  130  gm.  of  solution  contains 
30  gm.  of  salt.  From  this  we  then  calculate  that  100  gm.  of  solution 
would  contain  100/130X30  gm.,  or  23.08  gm.  of  salt.  This  corresponds 
with  (2) .  Suppose,  on  the  other  hand,  we  have  the  above  data  and  wish 
to  calculate  (3).  We  know  the  number  of  grams  of  salt  dissolved  in 
100  gm.  of  water  and  in  100  gm.  of  solution,  but  we  do  not  know  the 
weight  of  salt  in  100  cc.  of  solution.  Therefore  we  cannot  calculate 
either  the  weight  in  grams  or  the  number  of  moles  in  1  liter  of  solution. 
If  we  know  the  density  of  the  solution  we  are  in  a  position  to  calculate  the 
volume  of  solution  containing  a  known  weight  of  salt,  and  then  con- 
versely to  calculate  the  weight  or  number  of  moles  of  salt  in  1  liter. 
If,  for  example,  the  density  of  the  above  solution  is  1.175,  100  gm. 
of  solution  will  then  occupy  100/1.175,  or  85.1  cc.  But  we  know  that 
this  85.1  cc.  of  solution  contains  23.08  gm.  of  salt.  From  this  we  cal- 
culate by  proportion  that  1  liter  of  solution  would  contain  1000/85.  IX 
23.08  gm.  or  271  gm.  This  weight  divided  by  the  molar  weight  will 
give  the  number  of  moles  per  liter  of  solution. 

Solubility  of  Gases  in  Liquids. — The  solubility  of  a  gas  depends  on 
the  same  factors  as  does  the  solubility  of  a  solid;  namely,  the  tendency 
of  the  molecules  to  leave  their  associates  and  enter  the  solution,  and  the 
specific  attraction  of  the  solvent  molecules.  In  the  case  of  a  solid  the 
first  factor  is  practically  a  constant  because  the  concentration  of  a  solid 
cannot  be  appreciably  changed.  But  in  the  case  of  a  gas  this  factor  can 
be  varied  at  will.  Thus  we  may  determine  the  solubility  of  a  gas  at  a 
pressure  of  one  atmosphere,  or  two  atmospheres,  or  at  any  pressure.  If, 
then,  one  of  the  factors  governing  solubility  is  fixed  and  the  other  vari- 


SOLUBILITY  OF  LIQUIDS  IN   LIQUIDS  143 

able,  we  should  expect  the  solubility  to  be  proportional  to  the  intensity 
of  the  variable  factor.  This  is  exactly  what  we  find,  for  the  solubility 
of  gases  is  in  most  cases  proportional  to  the  pressure,  which  is  the  vari- 
able factor.  This  fact  is  known  as  Henry's*  Law  (discovered  in  1803). 
According  to  this  law,  if  a  gas  has  a  certain  solubility  at  a  pressure  of  one 
atmosphere  its  solubility  will  be  doubled  at  two  atmospheres,  etc. 

In  saying  that  the  solubility  of  a  gas  is  proportional  to  the  pressure, 
we  are  referring,  of  course,  to  solubility  by  weight,  as  specified  in  definition 
of  solubility  above.  So  far  as  volume  is  concerned  pressure  has  no  effect, 
within  reasonable  range,  on  the  solubility  of  a  gas.  If  10  volumes  of  a 
gas  dissolve  at  one  atmosphere  pressure,  10  volumes  -will  dissolve  at 
two  atmospheres,  etc.  It  should  be  noted,  however,  that  10  volumes 
of  a  gas  at  two  atmospheres  pressure  really  means  twice  as  much  gas  as 
10  volumes  at  one  atmosphere. 

In  this  connection  the  solubility  of  mixed  gases  is  interesting.  If  we 
have  a  mixture  of  two  gases  whose  intrinsic  solubility  (the  attraction  of 
the  solvent)  is  the  same,  we  should  expect  the  amount  of  each  gas 
dissolved  to  be  exactly  proportional  to  its  partial  pressure.  Thus  the 
partial  pressure  of  nitrogen  in  the  air  is  about  four-fifths  of  one 
atmosphere  and  that  of  the  oxygen  about  one-fifth.  If,  then,  the  solu- 
bilities of  these  two  gases  are  the  same,  we  should  expect  dissolved 
air  to  be  made  up  of  four-fifths  nitrogen  and  one-fifth  oxygen.  By 
experiment  it  is  found,  however,  that  air  which  has  been  dissolved 
in  water  and  then  expelled  by  boiling  is  composed  of  two-thirds  nitro- 
gen and  one-third  oxygen  by  volume.  So  we  must  conclude  that 
oxygen  is  simply  more  soluble  than  nitrogen,  other  things  being  equal. 

It  should  be  noted  in  passing  that  the  extremely  soluble  gases,  like 
ammonia  and  hydrogen  chloride,  do  not  obey  Henry's  law  in  the  matter 
of  solubility;  their  solubility  is  not  proportional  to  the  pressure.  This 
is  undoubtedly  due  to  the  fact  that  in  these  cases  a  compound  is 
formed  between  the  solute  and  the  solvent.  Thus  NHy  unites  with 
water  to  form  NH4OH,  and  HC1  unites  with  water  to  form  a  hydrate 
HC1-H2O. 

Solubility  of  Liquids  in  Liquids. — Under  this  head  we  meet  two  cases; 
first,  the  case  where  solubility  is  limited  as  in  the  case  of  solids  and  gases; 
and  the  second,  the  case  of  unlimited  solubility  where  solute  and  solvent 
may  be  mixed  in  all  proportions.  These  two  cases  are  often  spoken 
of  as  "  partial  miscibility,"  and  "  total  miscibility,"  respectively.  A 
mixture  of  ether  and  water  serves  as  an  example  of  partial  miscibility; 
100  gm.  of  water  at  a  temperature  of  19°  C.  dissolves  6.86  gm.  of  ether, 

*  William  Henry  (1774-1836),  a  physician  and  manufacturing  chemist  of  Man- 
chester, England. 


144     SOLUBILITY  AND  SUPERS ATUR ATIO N :   CONCENTRATION 

and  100  gm.  of  ether  dissolves  1.21  gm.  of  water.*  If  we  mix  together 
equal  amounts  of  ether  and  water  and  shake  the  mixture,  the  two  liquids 
will  saturate  each  other  in  the  proportions  above  mentioned,  and  if 
the  mixture  is  then  allowed  to  stand  the  two  solutions  will  separate  into 
two  distinct  layers,  the  ether  layer  being  at  the  top  because  of  its 
lower  density.  Alcohol  and  water  serve  as  an  example  of  complete 
miscibility,  since  these  two  liquids  may  be  mixed  in  all  proportions. 

Solubility  of  Fine  Powders. — We  have  defined  saturation  as  a  con- 
dition of  equilibrium  between  solid  and  solution,  and  have  seemed  to 
imply  that  it  made  no  difference  whether  the  solid  was  in  the  state  of  a 
fine  powder  or  in  pieces  of  measurable  size.  The  work  of  Hulettf 
and  others  has  shown  that  in  the  case  of  slightly  soluble  substances,  like 
calcium  sulphate  and  barium  sulphate,  the  size  of  the  particles  is  an 
important  factor.  Thus,  the  solubility  of  barium  sulphate  in  particles 
of  average  diameter  10"4  mm.  was  found  to  be  almost  twice  as  great  as 
that  of  the  same  material  in  particles  of  average  diameter  18  X 10"4  mm. 
This  may  be  explained  as  follows :  The  particles  of  the  solid  are  pressed 
upon  by  the  surface  tension  of  the  water  surrounding  them,  and  this 
surface  tension,  literally  "  squeezes  "  the  particles  into  solution.  On 
account  of  their  relatively  greater  surface,  this  action  has  a  more 
marked  effect  on  the  solubility  of  the  smaller  particles.  Hence  a  solu- 
tion saturated  over  extremely  fine  particles  will  have  a  higher  con- 
centration, than  one  saturated  over  coarse  particles.  If  a  solution  is  in 
contact  with  both  fine  and  coarse  particles  the  fine  particles  will  go  into 
solution,  making  the  solution  supersaturated  with  respect  to  the  larger 
particles.  Material  will  then  be  deposited  on  the  latter  and  they  will 
grow  still  larger.  The  net  result  will  be  a  disappearance  of  the  smallest 
particles  and  an  increase  in  the  size  of  the  largest  ones.  It  is  because  of 
this  tendency  that  a  precipitate  of  barium  sulphate  left  in  contact  with 
its  solution  for  some  time  becomes  filterable,  although  at  the  start 
many  of  the  particles  were  fine  enough  to  pass  through  a  paper.  This 
process,  when  hastened  by  heating,  is  spoken  of  as  "  digesting." 

Solubility  and  Temperature. — The  solubility  of  solids  usually  in- 
creases with  rise  in  temperature,  although  there  are  exceptions  to  this 
rule.  Thus,  the  solubility  of  calcium  sulphate  increases  with  rise  in  tem- 
perature until  the  temperature  of  34°  C.  is  reached,  and  then  decreases 
with  further  rise.  The  solubility  of  sodium  chloride  is  scarcely  affected 
at  all  by  change  in  temperature. 

The  solubility  of  liquids  in  liquids  usually  increases  with  rising  tem- 

*Klobbie,  Zeitschr.  physikal.  Chemie,  24,  619. 

t  Zeitschr.  physikal.  Chemie,  37,  384  (1901).  [George  A.  Hulett  (1867-  ), 
Professor  of  Physical  Chemistry,  Princeton  University.] 


SOLUBILITY  AND   TEMPERATURE 


145 


perature;  but,  just  as  in  the  case  of  solids,  some  exceptions  are  known. 
In  some  cases,  two  liquids  which  show  a  limited  solubility  at  ordinary 
temperatures  become  miscible  in  all  proportions  at  some  higher  tem- 
perature. The  temperature  at  which  this  occurs  is  called  the  "  critical 
solution  temperature."  The  following  examples  may  be  noted:  The 
solubility  of  water  in  ether  rises  with  temperature  and  the  solubility 
of  ether  in  water  decreases.  The  decrease  in  the  solubility  of  ether  is 
probably  due  to  its  great  volatility.  The  solubility  of  aniline  in  water 
and  that  of  water  in  aniline  both  increase  with  rising  temperature, 
and  at  165°  C.,  the  two  liquids  become  completely  miscible.  A  mixture 
of  phenol  (carbolic  acid)  and  water  follows  the  same  rule.  Thus,  at 
20°  C.  water  may  be  dissolved  in  phenol  until  the  solution  contains 
28  per  cent  water.*  Any  more  water  will  cause  the  formation  of  two 
layers.  On  the  other  hand,  phenol  may  be  dissolved  in  water  until  at 
20°  C.  the  solution  contains  8.3  per  cent  phenol,  and  more  phenol  will 
cause  the  formation  of  two  layers.  At  68.3°  C.  phenol  and  water  may 
be  mixed  in  all  proportions,  this  being  the  critical  point. 

The  solubility  of  gases  is  always  lowered  with  rising  temperatures. 
When  a  solvent  is  boiled,  gases  are  usually  entirely  expelled  from  it, 
although  this  is  not  always  the  case.  When,  for  example,  a  very  con- 
i  centrated  solution  of  hydrochloric  acid  is  boiled,  the  excess  of  gas 
•  (HC1)  is  driven  off  until  the  concentration  reaches  a  certain  point,  after 
which  the  solution  distills  unchanged,  the  distillate  having  the  same 
composition  as  the  boiling  solution,  f  It  is  interesting  to  note  that  a 
very  dilute  solution  of  hydrochloric  acid  becomes  more  concentrated 
on  boiling,  and  finally  reaches  the  same  composition  as  the  other.  This 
is  not  contrary  to  the  statement  that  rising  temperature  lowers  solu- 
bility, for  if  we  were  to  prepare  saturated  solutions  of  HC1  gas  at  0°, 

*  Seidell,  Solubilities  of  Inorganic  and  Organic  Compounds,  p.  479  (1919). 

t  The  composition  of  this  "constant  boiling  "  acid  is  so  accurate  that  the  method 
is  often  used  in  preparing  a  standard  solution.  See  Hulett  and  Bonner,  Jour.  Am. 
Chem.  Soc.,  31,  390.  The  following  data  are  taken  from  this  paper: 


Gm.  of  Solution 

Pressure,  mm. 

Per  Cent  HC1. 

Containing  1  Mol. 
HC1. 

770 

20.218 

180  .  390 

760 

20  .  242 

180.170 

750 

20.266 

179.960 

740 

20  .  290 

179  .  745 

730 

20.314 

179.530 

146      SOLUBILITY  AND  SUPERSATURATION :   CONCENTRATION 

20°,  30°,  etc.,  we  should  find  the  solubility  decreasing.     The  solution  we 
are  considering  above  is  not  saturated  at  the  lower  temperatures. 

Solubility  Curves. — In  the  case  of  solid  substances  it  is  customary 
to  determine  the  solubility  at  short  intervals  of  temperature  through  a 
considerable  range,  and  then  plot  the  values  on  coordinate  paper.  We 


10°       20°       30°      40-       50"       60°       70°      80°       90°      100° 
Temperature 

FIG.  25.— Solubility  Curves. 

thus  obtain  solubility  curves,  which  picture  to  the  eye  not  only  the 
relative  solubility  of  different  substances  but  also  the  effect  of  tempera- 
ture on  their  solubility.  A  steep  curve  indicates  that  change  in  tem- 
perature has  a  marked  effect;  a  flat  curve  indicates  the  opposite.  A 
sudden  break  in  a  curve  indicates  a  change  in  composition,  such  as  loss 
of  water  of  hydration.  The  above  chart  gives  the  solubility  curves 
for  several  common  salts.  The  striking  difference  in  the  solubility 


SOLID  SOLUTIONS  147 

of  potassium  iodide  and  potassium  perchlorate  can  be  seen  at  once, 
also  the  difference  in  steepness  of  the  curves  for  sodium  chloride  and 
potassium  nitrate.  Note  also  the  break  in  the  curve  for  sodium  sulphate 
where  the  hydrate  loses  its  water  and  changes  over  to  the  anhydrous 
salt. 

Solubility  curves  such  as  these  furnish  data  concerning  the  pos- 
sibility of  separating  salts  from  a  mixture  by  the  process  of  fractional 
crystallization.  Such  separation  will  be  possible  in  general  only  when 
the  solubility  curves  for  the  individual  salts  in  the  mixture  are  quite 
dissimilar.  Those  for  sodium  chloride  and  potassium  nitrate  are  exam- 
ples. Change  of  temperature  has  little  effect  on  the  solubility  of  sodium 
chloride  but  a  very  marked  effect  on  that  of  potassium  nitrate.  If, 
therefore,  a  solution  containing  the  two  salts  is  evaporated  at  a  high 
temperature  the  tendency  will  be  for  the  sodium  chloride  to  crystallize 
out  and  for  the  potassium  nitrate  to  remain  in  solution.  If  the  residual 
solution  (the  "  mother  liquor  ")  is  then  cooled  to  a  low  temperature,  the 
potassium  nitrate  crystallizes  out  and  the  sodium  chloride  remains  in 
solution.  In  this  way,  by  successive  evaporations  and  coolings,  a  very 
complete  separation  can  be  made. 

Solid  Solutions. — We  ordinarily  think  of  solution  as  referring  only 
to  liquids,  but  it  is  now  a  well-known  fact  that  substances  dissolve  not 
alone  in  liquids,  but  also  in  solids.  Such  solutions  are  called  "  solid 
solutions,"  and  they  show  all  the  important  characteristics  of  liquid 
solutions,  such,  for  example,  as  diffusion,  saturation,  etc.  We  can 
present  only  a  few  interesting  examples: 

A  class  of  minerals  called  "  zeolites  "  have  been  found  to  contain 
dissolved  water.*  These  minerals  are  transparent  and  homogeneous; 
but  the  water  is  present  in  indefinite  amounts  and  may  even  be  partially 
removed  without  altering  the  nature  of  the  mineral.  If  it  were  present 
as  water  of  hydration  it  would  be  possible  to  write  for  the  mineral  a 
definite  formula  containing  a  definite  number  of  molecules  of  H^O,  and 
its  removal  would  change  the  appearance  and  nature  of  the  mineral 
in  a  fundamental  way.  Since  this  does  not  occur  we  must  conclude 
that  the  water  is  merely  dissolved  in  the  mineral. 

Hydrogen  dissolves  in  metallic  palladium  until  the  metal  contains 
about  one  thousand  times  its  own  volume  of  the  gas.  At  elevated 
temperatures  the  gas  also  easily  diffuses  through  the  metal,  a  process 
characteristic  of  solutions  in  general.  Berthellot  f  found  that  oxygen 
and  nitrogen  gases  pass  through  the  walls  of  glass  tubes  when  these 
tubes  are  heated  to  the  softening  point  of  the  glass,  and  Belloc  J  found 

*  Zirkel,  Elemente  der  Mineralogie,  p.  733. 

t  Compt.  rend.,  140,  1159,  1286  (1905).          {  Compt.  rend.,  140.  1253. 


148     SOLUBILITY  AND  SUPERSATURATION :   CONCENTRATION 

that  oxygen  would  pass  through  the  walls  of  a  quartz  tube  even  at 
600°  C.,  a  temperature  which  is  far  removed  from  the  melting  point  of 
this  material. 

It  has,  for  centuries,  been  known  that  iron  absorbs  carbon  when 
heated  to  a  high  temperature  in  contact  with  it,  and  some  of  the  well- 
known  commercial  processes  of  working  iron  depend  on  this  fact. 
Hardened  steel  is  nothing  more  than  a  solid  solution  of  iron  carbide, 
FesC,  in  iron.  In  the  process  of  tempering,  the  iron,  containing  per- 
haps 0.8  per  cent  of  carbon  (  =  12  per  cent  FesC),  is  heated  to  a  tem- 
perature above  875°  C.  At  this  temperature  the  carbide  dissolves  in 
the  iron.  If  the  iron  is  allowed  to  cool  slowly  this  carbide  comes  out  of 
solution  in  the  form  of  minute  crystals,  which  can  be  seen  under  the 
microscope.  If,  however,  the  hot  iron  is  suddenly  cooled  ("  quenched  ") 
by  plunging  into  water  or  oil,  the  carbide  remains  in  solution,  and  the 
steel  thus  formed  is  seen  under  the  microscope  to  be  perfectly  homo- 
geneous. It  is  then  a  solid  solution,  and  is  valuable  because  it  happens 
to  possess  the  property  of  being  hard.  If  a  hardened  steel  tool  is  heated 
by  friction  or  otherwise  the  carbide  again  comes  out  of  solution.  Since 
the  pure  iron  is  much  softer  than  the  solution  the  steel  is  then  said  to 
have  "  lost  its  temper."  The  process  of  "  annealing  "  is  like  this  and 
gives  the  same  results. 

In  the  process  of  "  case  hardening,"  iron  is  heated  in  contact  with 
carbon  until  a  considerable  amount  of  the  latter  dissolves  in  the  surface 
layer.  The  iron  thus  treated  is  then  "  tempered,"  whereupon  the  sur- 
face layer  becomes  a  hard  solution  of  carbide  while  the  inner  core  remains 
soft  and  tough. 

A  saturated  solution  of  carbide  in  iron  contains  25.5  per  cent  FesC, 
equivalent  to  1.7  per  cent  carbon.*  Anything  in  excess  of  this  amounl 
will  crystallize  out,  either  as  carbide  or  as  free  carbon  (graphite). 

Another  interesting  example  of  solid  solution  is  seen  in  the  case  of 
piece  of  zinc  plated  with  copper.     When  the  plate  is  first  put  on  it  has 
the  true  copper  color  and  is  pure  copper,  but  after  a  time  it  becomes 
yellow  and  is  then  found  to  have  changed  into  brass.     The  zinc  has  gone 
into  solution  in  the  copper  and  vice  versa. 

Supersaturated  Solutions. — We  have  defined  saturation  as  a  state 
of  equilibrium  between  the  rate  of  solution  and  the  rate  of  return  to 
the  solid  (or  liquid)  condition.  In  order  that  such  an  equilibrium  may 
exist  it  is  evident  that  two  things  are  required:  first,  a  solution  whose 
concentration  has  the  saturation  value,  and  second,  the  presence  of  the 
solid  with  which  an  exchange  of  molecules  may  take  place.  If  either 
of  these  factors  is  wanting  there  can  be  no  such  thing  as  equilibrium. 
*  Mahin,  Quantitative  Analysis,  p.  481  (1919). 


SUPERSATURATED   SOLUTIONS 


149 


Thus,  if  in  the  presence  of  the  solid  the  concentration  of  the  solution  is 
less  than  the  saturation  value,  molecules  will  enter  the  solution  more 
rapidly  than  they  can  return  to  the  solid.  If  the  concentration  of  the 
solution  is  greater  than  the  saturation  value  molecules  will  return  to 
the  solid  faster  than  they  can  enter  the  solution.  In  the  absence  of  the 
solid  the  concentration  of  the  solution  may  be  either  above  or  below 
the  saturation  value  and  may  remain  so  indefinitely;  but  this  is  not 
a  case  of  equilibrium,  for  there  can  be  no  balancing  of  rates  of  action 
where  no  action  exists. 

The  state  of  non-equilibrium,  in  which  the  solution  contains  more 
than  the  saturation  amount  of  dissolved  substance,  is  called  "  super- 


^ 


-/ 


7 


Na2SO4  .7E 


4.10H20 


80° 


90°      100° 


0J        10°      20°       30°      40°      50°      60°      70 
Temperature 

FIG.  26. — Solubility  curves  of  sodium  sulphate. 

saturation."  Since  this  condition  exists  permanently  only  in  the 
absence  of  the  solid,  it  is  a  condition  easily  upset,  and  for  that  reason 
is  said  to  be  "  metastable."  The  least  particle  of  the  given  solid 
dropping  into  such  a  solution  instantly  starts  the  exchange  of  molecules; 
and  naturally,  considering  the  high  concentration  of  the  solution,  the 
solid  receives  molecules  much  more  rapidly  than  it  can  give  them  off. 
The  amount  of  solid  thus  increases  rapidly,  and  the  concentration  of  the 
solution  diminishes  until  the  ordinary  conditions  of  saturation  are 
reached. 

Causing  crystallization  by  dropping  into  the  solution  a  particle  of 
the  dissolved  solid  is  called  "  inoculation,"  or  "  seeding."  The  same 
effect  may  often  be  brought  about  by  violent  stirring  or  by  scratching 
the  inside  of  the  container,  and  still  more  surely  by  means  of  some  for- 


150      SOLUBILITY  AND  SUPERSATURATION :   CONCENTRATION 

eign  substance  which  happens  to  have  the  same  crystalline  form  as  the 
solute. 

A  good  example  of  supersaturation  is  the  case  of  sodium  sulphate. 
This  salt  very  readily  forms  supersaturated  solutions  because  it 
exists  in  three  distinct  forms  which  possess  different  degrees  of  solu- 
bility. These  forms  are:  the  anhydrous  salt,  Na2S(>4,  the  decahydrate, 
Na2SO4-10H20,  and  the  heptahydrate,  Na2SO4-7H2O.  The  sketch 
on  page  149  shows  the  solubility  curves  for  these  three  forms. 

The  dotted  part  of  the  upper  curve  indicates  that  it  is  possible  to 
obtain  saturated  solutions  of  the  anhydrous  salt  below  32.4°  C.,  con- 
taining the  amounts  of  solid  represented,  but  that  such  solutions  are 
in  the  metastable  condition.  If  the  hydrates  did  not  exist  such  solu- 
tions would  be  perfectly  stable;  but  since  they  do  exist,  and  their  sol- 
ubility below  32.4°  is  less  than  that  of  the  anhydrous  salt,  there  is  always 
a  tendency  for  them  to  appear.  The  solution  is  in  equilibrium  with  the 
anhydrous  salt  but  is  supersaturated  with  respect  to  the  hydrates, 
and  the  presence  of  a  trace  of  either  of  the  latter  will  always  cause  pre- 
cipitation. This  can  be  seen  by  inspection  of  the  curves.  Suppose,  for 
example,  60  gm.  of  anhydrous  salt  were  dissolved  in  100  gm.  of  water, 
as  plotted  at  the  point  A  on  the  curve.  This  would  be  at  15°  C.  At 
this  temperature  the  solubility  of  the  heptahydrate  is  only  40  gm.  and 
that  of  the  decahydrate  only  25  gm.  Moreover,  60  gm.  of  anhydrous 
salt  would  represent  about  110  gm.  of  heptahydrate  and  about  140  gm. 
of  decahydrate.  Evidently,  then,  such  a  solution  would  be  immensely 
supersaturated  with  reference  to  either  hydrate.  If,  therefore,  a  par- 
ticle of  heptahydrate  fell  into  the  solution,  this  salt  would  immediately 
crystallize  out  until  only  40  gm.  were  left.  Even  then  the  solution 
would  still  be  supersaturated  with  reference  to  the  decahydrate,  and 
would  yield  crystals  of  this  salt  if  a  particle  of  it  were  added. 

As  can  be  seen  by  reference  to  the  curves,  the  degree  of  supersatura- 
tion for  the  decahydrate  is  always  greater  than  that  for  the  heptahydrate. 
In  spite  of  this  fact  the  latter  salt  is  the  one  more  likely  to  separate  out 
under  these  conditions.  It  simply  cannot  stand  so  great  a  degree  of 
supersaturation  as  the  former.  Indeed,  if  this  solution  is  allowed  to 
stand  even  at  10°  for  a  few  hours,  the  excess  of  heptahydrate  will  usually 
crystallize  out  spontaneously,  leaving  the  solution  still  supersaturated 
with  respect  to  the  decahydrate. 

Preparation  of  a  Supersaturated  Solution. — The  above  considera- 
tions teach  us  that  the  general  method  of  preparing  supersaturated  solu- 
tions is  to  saturate  at  rather  high  temperatures,  remove  all  traces  of  the 
solid  by  filtering  or  otherwise,  and  then  cool  the  solution  to  a  tempera- 
ture at  which  the  solubility  of  the  given  salt  would  be  less  than  the 


MOLAR  AND  NORMAL  CONCENTRATION  151 

amount  in  the  solution.  This  method  applies  in  almost  any  case  where  a 
supersaturated  solution  can  be  obtained  at  all,  but  it  should  be  noted 
that  a  high  degree  of  supersaturation  can  be  obtained  in  only  a  few  cases. 
In  general,  a  slight  degree  of  supersaturation  immediately  results  in 
spontaneous  precipitation. 

Another  method  of  producing  supersaturated  solutions  is  to  bring 
about  some  chemical  reaction  which  will  produce  a  substance  in  amounts 
greater  than  can  ordinarily  remain  in  solution.  If  this  product  is  a 
substance  which  can  give  a  supersaturated  solution,  such  a  solution 
should  in  this  way  be  produced.  This,  of  course,  presupposes  the 
absence  of  every  trace  of  the  given  substance  in  solid  form,  for  any 
such,  if  present,  will  immediately  cause  precipitation. 

Still  another  method  of  producing  supersaturation  has  already  been 
indicated  in  our  discussion  of  steel  and  the  tempering  process.  We 
noted  that  if  the  solution  of  carbide  in  iron  were  allowed  to  cool  slowly 
the  carbide  crystallized  out.  It  stands  to  reason,  of  course,  that  this 
could  not  produce  less  than  a  saturated  solution  at  the  lower  tempera- 
ture; but  we  showed  also  that  if  the  solution  were  cooled  very  quickly 
much  more  carbide  remained  in  solution.  Such  a  solution,  then,  must 
be  strongly  supersaturated.  We  note,  however,  one  important  differ- 
ence between  this  form  of  supersaturation  and  the  ordinary  liquid  form. 
The  presence  of  the  solute  in  solid  form  does  not  cause  precipitation. 
The  explanation  is  that,  although  the  change  is  undoubtedly  occurring, 
it  is  doing  so  at  ordinary  temperatures  with  extreme  slowness;  with 
such  slowness,  indeed,  that  several  million  years  would  be  necessary  for 
the  completion  of  the  process. 

Molar  and  Normal  Concentration. — We  have  already  noted  that 
solubility — the  concentration  of  a  saturated  solution — may  be  expressed 
either  in  physical  units,  grams,  or  in  chemical  units,  moles.  The  latter 
mode  of  expression  has  a  decided  advantage  in  chemistry,  for  all  our 
chemical  reactions  involve  a  comparison  of  moles  rather  than  of  grams. 
Now,  we  must  note  that  the  concentration  of  any  solution,  whether 
saturated,  unsaturated,  or  supersaturated,  may  be  expressed  in  moles; 
and  just  as  in  the  case  of  a  saturated  solution,  here  also  it  is  customary 
to  state  the  concentration  in  moles  per  liter.  A  solution  containing  1 
mole  of  solute  in  1  liter  of  solution  is  said  to  be  "  molar,"  or  the  concen- 
tration stated  in  moles  is  said  to  be  "  1."  If  a  solution  contains  0.6 
mole  of  solute  in  1  liter  the  concentration  is  0.6. 

Notice  that  a  molar  solution  contains  1  mole  of  solute  in  1  liter  of 
solution,  not  1  liter  of  water.  To  make  1  liter  of  molar  solution,  we  weigh 
out  1  mole  of  the  substance  and  then  add  sufficient  water  to  make  1  liter 
of  solution  after  the  substance  is  dissolved.  Thus,  to  make  1  liter  of 


152       SOLUBILITY  AND  SUPERSATURATION :   CONCENTRATION 

molar  sodium  chloride  we  weigh  out  58.5  gm.  of  the  solid,  dissolve  it  in  a 
little  water,  and  then  make  up  the  solution  to  1  liter  by  adding  water. 
We  do  not  use  a  liter  of  water  altogether,  because  the  solid  occupies  some 
space  even  after  it  is  dissolved. 

It  is  also  customary  to  state  in  moles,  not  alone  the  concentration  of 
compounds,  but  also  that  of  the  radicals  contained  within  them.  Sup- 
pose, for  example,  we  have  a  solution*  of  copper  nitrate,  Cu(NOs)2. 
We  state  its  concentration  as  a  whole  as  so  many  moles  per  liter,  and  we 
may  also  state  the  concentration  of  the  copper  and  of  the  nitrate  radicals 
in  the  same  way.  The  concentration  of  the  copper  radical,  Cu,  will  be 
the  same  as  that  of  the  nitrate  as  a  whole,  for  each  mole  of  copper  nitrate 
contains  1  mole  of  copper  radical.  Thus,  if  the  solution  contains  3 
moles  of  copper  nitrate,  the  concentration  of  the  salt  as  a  whole  is  3; 
but  the  solution  also  contains  3  moles  of  copper  radical  per  liter,  1  for 
each  mole  of  the  salt,  and  so  the  concentration  of  the  copper  radical  is 
also  3.  But  each  mole  of  copper  nitrate  contains  2  moles  of  the  nitrate 
radical,  NOs,  so  the  concentration  of  this  radical  will  be  twice  that  of  the 
salt  as  a  whole,  and  twice  that  of  the  copper  radical.  If  the  concen- 
tration of  the  salt  is  3,  that  of  the  nitrate  radical  is  6. 

One  of  the  most  important  points  to  remember  with  reference  to 
molar  solutions  is  that  "  equimolar "  means  also  "  equimolecular." 
By  this  we  mean  that  if  two  solutions  have  the  same  molar  concentra- 
tion they  will  contain  the  same  absolute  number  of  molecules  in  equal 
volumes.  Thus,  1  liter  of  molar  hydrochloric  acid  contains  the  same 
number  of  molecules  as  1  liter  of  molar  copper  nitrate.*  When  we  come 
to  the  subject  of  equilibrium  where  concentration  is  an  important  factor, 
we  shall  find  a  thorough  appreciation  of  this  fact  very  useful. 

In  volumetric  analytical  work,  concentration  is  usually  stated  in 
terms  of  equivalents.  When  we  state  it  thus,  we  have  what  is  termed 
normal  concentration.  A  normal  solution  is  one  which  contains  1  gram- 
equivalent  weight  of  solute  in  1  liter  of  solution.  Thus,  a  normal  solution 
of  sodium  contains  23  gm.  of  sodium  per  liter;  a  normal  solution  of  ferric 
iron  contains  56  gm.  of  iron  per  liter. 

The  normal  solution  of  a  compound  contains  in  1  liter  such  a  weight 
of  the  compound  as  will  react  with  one  equivalent  weight  of  an  element. 
In  the  case  of  a  salt  this  would  be  the  weight  of  the  salt  which  would 
contain  one  equivalent  weight  of  the  metal.  Incidentally,  this  would 
include  one  equivalent  weight  of  the  acid  radical  also,  because  the  metal 
and  the  acid  radical  are  always  combined  equivalent  for  equivalent. 
The  normal  solution  of  an  acid  would  contain  1  gm.  of  replaceable  hydro- 

*  We  are  not  considering  here  the  possibility  that  many  of  the  molecules  may  be 
ionized. 


MOLAR  AND  NORMAL  CONCENTRATION  153 

gen  per  liter;  that  of  a  base  one  equivalent  of  hydroxyl,  OH,  which 
amounts  to  17  gm.  The  normal  solution  of  an  oxidizing  or  reducing  agent 
contains  one  equivalent  weight  of  the  element  or  compound  acting  in  that 
capacity.  What  this  is  depends  on  the  oxidizing  or  reducing  valence. 
Thus,  in  the  case  of  nitric  acid  it  is  one-third  the  molecular  weight;  in 
the  case  of  ferrous  iron  it  is  the  whole  atomic  weight  of  the  iron. 

In  the  case  of  univalent  elements  and  compounds,  normal  concen- 
tration and  molar  concentration  are  identical;  but  where  the  valence 
is  more  than  one,  the  two  values  differ.  Thus,  a  normal  solution  of 
hydrochloric  acid  or  of  sodium  chloride  contains  one  mole  per  liter  and 
is  therefore  molar.  A  normal  solution  of  sulphuric  acid  or  sodium  car- 
bonate contains  half  a  mole  per  liter  and  is  therefore  half-molar. 

In  the  case  of  radicals  the  normal  concentration  is  always  the  ^ame 
as  that  of  the  compounds  of  which  the  radicals  are  a  part.  Take,  for 
example,  copper  nitrate  solution:  if  the  concentration  is  normal  with 
respect  to  the  salt  as  a  whole,  the  solution  contains  one  equivalent  of 
copper  per  liter;  and,  since  the  radicals  making  up  a  salt  can  unite  only 
equivalent  for  equivalent,  the  solution  contains  also  one  equivalent  of 
nitrate  radical.  Therefore  the  solution  is  normal  with  respect  to  both 
the  copper  and  the  nitrate  radical.  Note  how  this  differs  from  molar 
concentration  as  described  above. 

Since  any  two  substances  will  react  in  the  proportion  of  their  equiva- 
lent weights,  any  two  solutions  having  the  same  normality  (normal 
concentration)  will  react  volume  for  volume.  Thus  50  cc.  of  normal 
acid  (any  acid)  will  react  with  50  cc.  of  normal  base,  and  50  cc.  of  normal 
oxidizing  agent  will  react  with  50  cc.  of  normal  reducing  agent.  In 
making  calculations  involving  solutions  of  known  normality  this  fact 
should  always  be  utilized.  In  this  way  much  needless  work  can  be 
avoided.  The  following  examples  will  show  what  is  meant : 

1.  How  many  grams  of  sodium  chloride  will  be  required  to  precipitate  the  silver 
from  10  cc.  of  N/2  silver  nitrate  solution? 

In  solving  this  problem  we  remember  that  10  cc.  of  N/2  sodium  chlo- 
ride solution  will  be  required  to  react  with  10  cc.  of  N/2  silver  nitrate, 
and  simply  calculate  directly  the  weight  of  sodium  chloride  needed  for 
the  preparation  of  10  cc.  N/2.  This  will  be  the  weight  asked  for.  Thus, 
the  molecular  weight  of  NaCl  is  58.5  and  it  is  univalent.  Therefore  the 
weight  for  1000  cc.  N  is  58.5  gm.,  for  1000  cc.  N/2  it  is  29.25  gm  and 
for  10  cc.  it  is  0.2925  gm. 

2.  What  weight  of  sodium  carbonate  is  required  to  neutralize  25  cc.    of  N/4 
sulphuric  acid? 

Here  again  we  work  entirely  in  terms  of  the  required  substance,  not 


154      SOLUBILITY  AND  SUPERSATURATION :   CONCENTRATION 

in  terms  of  the  substance  with  which  it  reacts.  Thus,  the  molecular 
weight  of  sodium  carbonate  (Na2CO3)  is  106,  and  it  is  bivalent.  The 
weight  for  1000  cc.  N  is,  therefore,  53  gm.,  for  1000  cc.  of  N/4  it  is 
13.25  gm.,  and  for  25  cc.  N/4  it  will  be  1/40  of  13.25  gm.,  or  0.3312  gm. 
Procedures  like  these  should  be  employed  in  every  case  where  it  is 
required  to  calculate  the  weight  of  one  substance  which  will  react  with  a  given 
volume  of  some  solution  of  known  normality. 

EXERCISES 

1.  Explain  the  mechanism  of  solution  and  the  state  of  saturation. 

2.  Define  and  illustrate  several  methods  of  stating  solubility. 

3.  In  what  ways  does  the  solubility  of  gases  differ  from  that  of  solids?     What  is 
Henry's  law?     If  water  dissolves  its  own  volume  of  a  gas  at  one  atmosphere  pressure, 
what  volume  will  it  dissolve  at  two  atmospheres  pressure? 

4.  What  peculiarity  of  solubility  is  seen  in  the  case  of  fine  powders?     Give  an 
example.     Explain  the  peculiarity.     What  is  the  purpose  of  "  digesting,"  as  referred 
to  precipitates? 

6.  What  gases  do  not  follow  Henry's  law  in  respect  to  their  solubility? 

6.  What  is  meant  by  the  terms  "  partial  miscibility  "  and  "  total  miscibility  " 
as  referring  to  the  solubility  of  liquids. 

7.  In  what  general  ways  are  solubility  and  temperature  related?  .  Describe  the 
special  cases  of  ether  and  water,  aniline  and  water,  phenol  and  water,  and  hydrochloric 
acid  and  water. 

8.  Refer  to  Comey's  "  Dictionary  of  Solubilities,"  (1921),  pp.  579  and  839,  where 
will  be  found  the  solubility  data  for  potassium  nitrate  and  sodium  chloride  respect- 
ively.    Plot  the  data  on  coordinate  paper  for  the  temperatures  0°,  5°,  10°,  15°,  etc:, 
up  to  60°,  and  draw  a  smooth,  accurate  solubility  curve  for  each  salt.     Plot  both 
curves  on  the  same  paper  and  to  the  same  axes,  making  temperatures  abscissae  and 
grams  per  100  gm.  water  ordinates.     As  a  guide  in  drawing  the  curve  use  a  flexible 
celluloid  ruler. 

9.  Read  off  from  your  curve  the  solubilities  for  17°  and  36°,  and  compare  with  the 
values  given  in  the  book. 

10.  At  what  temperature  is  the  solubility  of  NaCl  and  KNO3  equal?     What  is 
the  solubility  at  this  temperature? 

11.  Ten  cc.  of  a  saturated  sodium  chloride  solution  weighed  12.003  gm.,  and 
when  evaporated  to  dryness  the  salt  was  found  to  weigh  3.173  gm.     Determine  the 
following: 

(a)  The  solubility  in  grams  per  100  gm.  of  water. 
(6)   The  percentage  solubility  by  weight. 

(c)  The  density  of  the  solution. 

(d)  The  molar  solubility. 

12.  Suppose  you  have  100  gm.  of  water  saturated  with  both  NaCl  and  KNOa 
at  35°  C.     Evaporate  50  gm.  of  water,  keeping  the  temperature  at  60°.     What 
weight  of  each  salt  will  crystallize  out?     Now  lower  the  temperature  of  the  "  mother 
liquor  "  to  0°  C.     What  weight  of  each  salt  will  crystallize  out? 

13.  Discuss  instances  in  which  gases  dissolve  in  solids. 

14.  Discuss  the  properties  of  tempered  steel  as  an  example  of   solid   solution. 
Explain  "  case  hardening." 


EXERCISES  155 

16.  Under  standard  conditions  the  solubility  of  oxygen  and  nitrogen  gases  in 
water  are  as  follows : 

Oxygen  0.0708  gm.  per  liter. 
Nitrogen  0.0291  gm.  per  liter. 

Calculate  the  weight  of  each  gas  which  would  be  present  in  a  liter  of  water  sat- 
urated with  air  under  standard  conditions,  counting  the  partial  pressure  of  the 
nitrogen  as  80  per  cent,  and  that  of  the  oxygen  as  20  per  cent,  of  the  total  pressure. 
From  the  weights,  calculate  the  volumes  of  the  two  gases  dissolved  as  they  would  be 
under  standard  conditions,  and  then  note  whether  these  volumes  are  related  as 
are  the  volumes  of  oxygen  and  nitrogen  in  the  air. 

16.  Define  the  state  of  supersaturation. 

17.  If  a  solution  has  been  standing  for  a  time  and  has  deposited  some  salt  crystals 
is  it  likely  to  be  still  supersaturated? 

18.  How  would  you  proceed  in  general  to  prepare  a  supersaturated  solution? 
How  avoid  supersaturation? 

19.  Trace  out  the  solubility  curves  for  sodium  sulphate  and  its  hydrates  and 
explain  each  part. 

20.  A  solution  saturated  with  sodium  sulphate  at  70°  C.  is  cooled  to  20°.     Is  this 
solution  now  supersaturated  with  respect  to  the  two  hydrates,  and,  if  so,  to  what 
extent? 

21.  Define  molar  concentration,  as  applied  to  compounds  and  radicals.      Exam- 
ples. 

22.  Define  normal  concentration,  as  applied  to  an  element,  a  salt,  an  acid,  a 
base,  or  to  radicals. 

23.  What  is  the  molar  concentration  of  the  SO4  in  normal  sulphuric  acid? 

24.  A  certain  sulphuric  acid  solution  has  a  normality  of  0.05.     What  is  its  molar 
concentration? 

26.  What  weight  of  anhydrous  sodium  carbonate,  Na2CO3,  is  required  for  200  cc. 
of  N/2  solution? 

26.  How  many  cubic  centimeters  of  hydrochloric  acid,  density  1.2,  containing 
39  per  cent  actual  HC1  by  weight,  are  required  for  1200  cc.  of  N/5  acid? 

27.  How  many  cubic  centimeters  of  N/2  acid  are  required  to  neutralize  1  gm.  of 
pure  sodium  carbonate? 

28.  A  certain  sulphuric  acid  solution  has  a  density  of  1.810,  and  contains  88.3 
per  cent  actual  H2SO4.     What  is  the  weight  of  100  cc.?     What  volume  is  occupied 
by  100  gm.?     How  many  cc.  must  be  used  to  make  1  liter  of  N/4  acid? 

29.  Two  hundred  cc.  of  a  zinc  chloride  solution  was  found  to  contain  10  gm.  of 
zinc.     What  was  the  normal  concentration? 

30.  Calculate  the  weight  of  HC1  present  in  400  cc.  of  acid  which  required  320  cc. 
of  N/4  NaOH  for  neutralization. 

31.  Calculate  the  normality  of  an  acid  600  cc.  of  which  when  acted  upon  by  an 
equivalent  amount  of  Na2CO3  evolved  under  standard  conditions  2100  cc.  of  CO2. 

32.  Five  liters  of  lime-water,  saturated  at  18°  C.,  contain  7.4  gm.  of  solid  Ca(OH)2. 
Calculate  the  molar  concentration  of:   (a)  the  Ca(OH)2,  (6)  the  Ca,  (c)  the  OH. 

33.  Consult  the  labels  on  the  1\  liter  bottles  of  concentrated  acids  for  the  density 
and  the  per  cent  of  acid  by  weight.     Calculate  the  normality  of  each. 

34.  A  concentrated  ammonia  solution  has  a  density  of  0.90  and  contains  28  per 
cent  NH3  by  weight.     Calculate  the  normality  in  terms  in  NH4OH.     (The  concen- 
tration as  NH4  is  the  same  as  that  of  the  NH3.) 


CHAPTER  XIII 


FREEZING-POINTS   AND    BOILING-POINTS    OF    SOLUTIONS: 
OSMOTIC  PRESSURE:    VAN'T  HOFF'S  GENERALIZATION 

Depression  of  Freezing-point. — It  is  a  fact  of  common  experience 
that  solutions  freeze  at  lower  temperatures  than  the  pure  solvents. 
When  a  dilute  water  solution  is  frozen,  ice  alone  separates  at  first.  As 
more  and  more  ice  separates  the  solution  becomes  more  and  more  con- 
centrated, and  the  freezing-point  falls  lower  and  lower.  Finally  a  point 
is  reached  where  the  solution  becomes  saturated,  and,  from  that  point 
on,  ice  and  solute  separate  together.  The  point  at  which  this  occurs  is 
called  the  "  cryohydric  point."  If  we  continue  to  freeze  such  a  solution 
the  temperature  remains  unchanged  until  the  whole  mass  has  solidified. 
The  cryohydric  point  for  a  solution  of  sodium  chloride  is  —22.4°  C., 
when  the  solution  contains  30  gm.  of  solid  NaCl  per  100  gm.  of  water. 
The  cryohydric  point  for  calcium  chloride  is  —55°  C.,  when  the  solution 
contains  42.5  gm.  of  solid  CaCl2  per  100  gm.  of  water.  When  ice  is 
mixed  with  a  solid  saltj  enough  ice  melts  to  form  a  saturated  solution  of 
the  salt,  and  the  temperature  of  the  solution  will  be  at  the  cryohydric 
point.  This  solution  is  in  equilibrium  with  the  ice,  and  is  ready  to 
deposit  both  ice  and  salt  if  heat  is  abstracted  from  it.  According  to 
this  the  lowest  temperature  we  can  expect  to  get  with  a  mixture  of  ice 
and  salt  is  —22.4°  C.  Calcium  chloride  would  evidently  be  better 
for  refrigerating  purposes. 

The  depression  of  the  freezing-point  noticed  in  solutions  is  best 
'  accounted  for  by  an  application  of  the  kinetic  theory.  The  freezing- 
point  of  a  pure  solvent  is  a  point  of  balance  between  the  kinetic  energy 
of  the  molecules,  tending  to  reduce  the  substance  to  a  liquid,  and  the 
force  of  cohesion,  tending  to  cause  an  arrangement  of  the  molecules  in 
the  form  of  solid  crystals.  In  the  case  of  solutions,  the  kinetic  energy 
is  aided  by  another  force,  namely,  the  attraction  of  the  solute  molecules 
for  those  of  the  solvent.  Evidently  to  bring  about  a  balance  in  this 
case,  the  kinetic  energy  of  the  molecules  must  be  reduced  to  a  lower 
point  than  in  the  case  of  the  pure  solvent ;  that  is,  the  temperature  must 
be  lower. 

156 


MOLECULAR  LOWERING 


157 


The  freezing-point  of  a  solution  is  governed  also  by  equilibrium  con- 
ditions with  the  vapor  phase.  This  may  be  explained  as  follows: 

We  have  seen  that  a  liquid  like  water  has  a  certain  vapor  pressure 
which  is  governed  by  the  temperature,  and  we  plot  a  curve  showing 
this  pressure  at  different  temperatures.  The  curve  for  water  is  seen  in 
the  sketch  (Fig.  27).  The  frozen  liquid  also  has  a  certain  vapor  pressure, 
and  this  is  also  governed  by  the  temperature.  The  curve  for  ice  is  seen 
plotted  below.  The  freezing-point  of  a  liquid  is  the  point  where  the 
two  curves  come  together,  the  point  A  in  the  sketch,  which  for  water  is 
at  0°  C.  At  this  point  the  vapor  pressures  of  solid  and  liquid  are  evi- 
dently equal.  If  they  were  not  equal,  and  if  a  mixture  of  solid  and 


(40° -20°      0°      20°     40°     60°     80°    100° 
Temperature 

FIG.  27  .i— Vapor  pressure  curves  for  water,  ice,  and  solution. 


liquid  were  kept  at  the  freezing-point  for  a  time,  either  the  solid  would  go 
completely  over-  into  the  liquid  form  or  the  liquid  would  become  all 
solid,  and  this  is  contrary  to  fact.  Now,  the  vapor  pressure  of  a  solu- 
tion is  found  always  to  be  lower  than  that  of  the  pure  solvent.  Hence, 
the  vapor  pressure  curve  of  a  solution  will  always  stand  lower  down 
than  that  of  the  corresponding  solvent.  Such  a  curve  for  a  water  solu- 
tion is  seen  in  this  sketch.  The  freezing-point  of  the  solution  will  be 
the  point  where  its  vapor  pressure  curve  meets  that  of  the  solid  solvent, 
and  that  point  will,  of  course,  be  below  the  freezing-point  of  the  pure 
solvent;  at  the  point  B,  for  example,  in  the  case  of  a  water  solution. 

Molecular  Lowering. — If  the  depression  of  the  freezing-point  is  due 
to  the  attraction  of  the  solute  molecules  we  may  expect  that  the  amount 


158      FREEZING-POINTS  AND  BOILING-POINTS  OF  SOLUTIONS 


of  this  depression  for  any  given  solvent  will  be  proportional  to  the 
number  of  solute  molecules  present.  We  are,  therefore,  not  surprised  to 
find  that  depression  of  the  freezing-point  is  proportional  to  the  number 
of  moles  of  solute  in  a  given  weight  of  solvent.  This  amounts  to  saying 
that  if  we  dissolve  a  mole  of  any  substance  in  1000  gm.  of  water,  the 
freezing-point  will  be  depressed  by  the  same  amount,  no  matter  what  the 
substance  is,  provided  only  that  the  water  does  not  in  any  way  act  upon 
it  to  change  its  nature  or  form.*  Thus  the  freezing-point  of  water  is 
lowered  1.86°  C.  if  in  1000  gm.  we  dissolve  1  mole  of  alcohol  (46  gm.), 
1  mole  of  sugar  (342  gm.),  1  mole  of  glycerin  (92  gm.),  or  1  rnole  of 
any  one  of  a  thousand  other  substances  which  we  might  mention.  The 
lowering  of  the  freezing-point  thus  caused  by  the  addition  of  1  mole  of 
solute  to  1000  gm.  of  solvent  is  called  the  "  molecular  lowering,"  or 
sometimes  the  "  freezing-point  depression  constant."  The  following 
table  gives  the  depression  constants  for  several  solvents: 

Acetic  acid 3 . 90° 

Benzene 5 . 00 

Ethyl  bromide 11 . 79 

Formic  acid 2 . 77 

Nitrobenzene 7 . 07 

Water 1.86 

Phenol 7.40 

Molecular  Weights. — It  will,  of  course,  be  seen  immediately  that  we 
have  in  the  freezing-point  depression  a  method  for  the  determination  of 
molecular  weights.  All  we  need  to  do  is  to  find  what  weight  of  a  given 
substance  must  be  dissolved  in  1000  gm.  of  a  given  solvent  to  lower  the 
freezing-point  by  the  amount  given  in  the  above  table.  The  freezing- 
point  method  is  easy  and  accurate,  and  for  practical  work  is  a  close  com- 
petitor of  the  Dumas  method.  This  is  partly  due  to  the  fact  that  it  is 
applicable  in  cases  where  a  compound  is  not  volatile,  while  the  Dumas 
method  is  not. 

For  the  development  of  the  principle  of  freezing-point  depression 
and  its  application  to  the  determination  of  molecular  weights,  we  are 
indebted  to  the  French  chemist  Raoult.  f  His  researches  also  included 
the  matter  of  boiling-point  rise,  which  we  shall  now  discuss.  The 
technique  of  the  work  was  very  much  improved  by  Beckman,  {  who 

*  Some  substances  unite  with  water  to  form  hydrates,  such  as  CaCl2-6H2O. 
Such  action  lowers  the  amount  of  solvent  and  thus  makes  the  solution  more  con- 
centrated. It  therefore  results  in  too  great  a  depression.  Sugar  seems  to  do  this  in  a 
slight  degree.  Some  substances  are  also  ionized  in  solution. 

t  Francois  M.  Raoult  (1832-1901),  Professor  of  Chemistry,  University  of  Gren- 
oble. 

t  Ernst  Beckman,  Professor  of  Physical  Chemistry,  University  of  Leipzig. 


BOILING-POINT  RISE  159 

invented  fine  freezing-point  and  boiling-point  apparatus,  including  a 
differential  thermometer  which  showed  differences  of  temperature  as 
small  as  0.001°  C. 

Boiling-point  Rise. — Since  the  principle  involved  in  the  rise  of  boiling- 
point  is  the  same  as  that  already  described  under  depression  of  freezing- 
point,  it  will  not  be  necessary  to  enter  into  great  detail.  The  boiling- 
point  of  a  solution  is  invariably  higher  than  that  of  the  pure  solvent, 
provided  only  that  the  solute  is  not  volatile.*  The  boiling-point  of  a 
water  solution  is,  in  general,  above  100°  C. 

The  explanation  here  is  exactly  the  same  as  in  the  case  of  the  freezing- 
point  depression.  The  boiling-point  of  a  liquid  is  the  temperature  at 
which  the  vapor  pressure  equals  the  atmospheric  pressure.  In  the  case 
of  a  solution,  the  solute  molecules,  by  their  attraction,  hold  back  the 
solvent  molecules  and  thus  prevent  their  going  into  the  vapor  state. 
Therefore,  to  bring  the  vapor  pressure  up  to  the  atmospheric  pressure 
requires  a  higher  temperature  than  is  required  in  the  case  of  the  pure 
solvent.  This  can  be  seen  by  inspection  of  the  vapor  pressure  curves 
given  in  Fig.  27.  The  point  C  is  the  point  where  the  vapor  pressure  of 
water  reaches  76  cm.,  and  the  point  D  is  the  same  point  for  the  water 
solution.  Note  that  D  lies  at  a  higher  temperature  than  C. 

As  in  the  case  of  the  freezing-point  depression,  the  rise  in  the  boiling- 
point  of  any  given  solvent  is  proportional  to  the  number  of  molecules 
of  solute  present  in  any  given  weight  of  solvent.  This  is  also  inde- 
pendent of  the  nature  of  these  molecules,  provided,  of  course,  they  are 
not  acted  upon  by  those  of  the  solvent.  Thus  the  presence  of  1  mole 
of  solute  in  1000  gm.  of  water  raises  the  boiling-point  0.52°  C.  The 
following  table  gives  the  boiling-point  constants  for  several  solvents: 

Acetic  acid 1 . 15° 

Ether 2.11 

Water 0.52 

Acetone 1 . 67 

Chloroform 3 . 67 

Benzene 2 . 67 

The  boiling-point  method  can,  of  course,  be  used  for  the  determina- 
tion of  molecular  weights,  and  is  so  used;  but  it  is  subject  to  greater 
likelihood  of  error  than  is  the  freezing-point  method,  simply  because  the 
temperatures  measured  are  usually  farther  from  the  ordinary  room  tem- 
peratures and  therefore  harder  to  control.  It  is  often  used,  however, 

*  The  boiling-point  of  a  solution  of  alcohol  in  water  is  lower  than  that  of  pure 
water,  because  the  alcohol  is  volatile  and  thus  makes  up  part  of  the  vapor  pressure. 
The  combined  vapor  pressure  of  the  alcohol  and  the  water  reaches  76  cm.  before 
100°  C.  is  reached. 


160       FREEZING-POINTS  AND  BOILING-POINTS  OF  SOLUTIONS 

particularly  in  those  cases  where  the  only  available  solvent  has  no 
easily  measurable  freezing-point. 

Osmotic  Pressure. — We  have  already  noted  that  when  a  substance 
dissolves  in  water  the  molecules  of  the  solute  diffuse  about  in  solution 
very  much  after  the  manner  of  gases.  We  have  now  to  note  that  if 
this  process  of  diffusion  in  solution  is  hindered  by  a  suitable  partition,  a 
pressure  is  developed.  Because  of  the  fact  that  this  pressure  tends  to 
push  or  distend  the  obstructing  partition  or  membrane,  it  is  called 
"  osmotic  "  from  the  Greek  OXT/AOS,  meaning  "  a  push."  The  process  by 
which  the  pressure  is  developed  is  called  "  osmosis." 

In  order  to  feel  and  measure  osmotic  pressure  it  is  necessary  to  have 
what  is  called  a  "  semi-permeable  "  partition  or  membrane,  and  to 
place  on  one  side  of  it  the  solution  and  on  the  other  the  pure  solvent. 
This  membrane  allows  the  free  passage  of  the  solvent  but  prevents  the 
passage  of  the  solute;  hence  the  name  "  semi-permeable."  Parch- 
ment paper  and  certain  animal  membranes  make  fairly  good  semi- 
permeable  membranes,  but  they  are  not  perfect  enough  for  quantitative 
work,  for  they  do  allow  a  slight  passage  of  solute  molecules.  To  obtain  a 
perfectly  semi -permeable  membrane  is  a  very  difficult  matter.  The 
best  one  made  up  to  date  is  of  copper  ferrocyanide;  but  this  is  an 
extremely  fragile  substance,  and  must  be  supported  to  prevent  rupture. 
This  is  accomplished  by  forming  the  membrane  inside  the  walls  of  a 
porous  cup  of  unglazed  porcelain.  A  dilute  solution  of  copper  sulphate 
is  placed  inside  the  cup,  and  the  latter  is  then  immersed  in  a  dilute 
solution  of  potassium  ferrocyanide.  The  two  solutions  diffuse  into  the 
walls  of  the  cell,  and  where  they  meet  they  form  a  membrane  of  copper 
ferrocyanide  perfectly  supported  by  the  network  of  clay. 

The  credit  for  the  discovery  of  the  ferrocyanide  membrane  belongs 
to  Traube  *  (1867);  but  Pfeffer,f  a  botanist,  originated  the  idea  of 
depositing  the  membrane  in  the  walls  of  a  porous  cup  and  also  made  the 
first  quantitative  measurements  of  osmotic  pressure  (1877).  The  form 
of  Pfeffer's  apparatus  is  represented  in  the  sketch  (Fig.  28). 

A  is  a  porous  cup,  having  the  ferrocyanide  membrane  deposited 
within  its  walls.  B  is  the  manometer  containing  mercury,  and  is  used 
to  measure  the  pressure.  When  in  use  the  apparatus  is  first  entirely 
filled  with  the  solution  to  be  tested,  even  to  the  surface  of  the  mercury 
in  C.  The  tube  D,  at  the  top,  is  then  sealed  off,  and  the  whole  appa- 
ratus, including  the  manometer,  is  immersed  in  a  bath  of  pure  water 

*Archiv.  f.  Anat.  u.  Physiol.,  p.  87  (1867).  [J.  Traube,  Technical  High  School, 
Berlin.] 

t  Osmotische  Untersuchungen,  Leipzig,  1877.  [Wilhelm  Pfeffer  (1845-1920), 
Professor  of  Botany,  University  of  Leipzig.] 


CAUSE  OF  OSMOTIC   PRESSURE 


161 


kept  at  a  constant  temperature.     The  water  at  first  passes  through  the 

membrane,  increasing  the  pressure  inside  the  apparatus  and  forcing  the 

mercury  up  the  manometer  tube.     After  a  time 

equilibrium  is  reached  and  the  pressure  no  longer 

increases.     The  maximum  then  read  off  on  the 

manometer  is  taken  as  the  osmotic  pressure  of  the 

solution. 

Cause  of  Osmotic  Pressure. — The  most  prob- 
able cause  *  of  osmotic  pressure  can  be  shown  by 
analogy.  At  280°  C.  hydrogen  gas  is  readily 
soluble  in  metallic  palladium,  forming  with  it  a 
solid  solution.  At  this  temperature,  nitrogen  is 
not  at  all  soluble  in  palladium.  If,  therefore,  we 
were  to  fill  a  palladium  flask  with  a  mixture  of 
hydrogen  and  nitrogen  under  atmospheric  pres- 
sure, and  then  immerse  it  in  an  atmosphere  of 
pure  hydrogen,  also  at  atmospheric  pressure,  we 
should  have  an  arrangement  analogous  to  that  of 
a  solution  separated  from  the  solvent  by  a  semi- 
permeable  membrane.  The  mixture  of  gases 
represents  the  solution,  the  single  gas  represents 
the  solvent,  while  the  metal,  being  permeable  to 
one  gas  and  not  to  the  other,  represents  the  semi- 
permeable  membrane.  With  this  arrangement  the  following  thing  hap- 
pens: Molecules  of  hydrogen  enter  the  metal,  forming  a  solution  with  it. 
The  ordinary  interchange  of  molecules  between  solution  and  gas  then 
begins.  But  the  hydrogen  molecules  diffuse  through  the  metal,  and 
some  of  them  then  come  off  the  inside  as  well  as  the  outside.  The  process 
continues  until  the  pressure  of  the  hydrogen  inside  the  flask  equals  the 
pressure  of  the  same  gas  outside.  All  this  time  the  nitrogen  has  remained 
in  the  flask  and  is  still  exerting  its  full  pressure.  Therefore  when 
equilibrium  is  established  the  pressure  will  have  been  increased  by  an 
amount  exactly  equal  to  the  pressure  of  the  nitrogen,  f 

Now,  since  osmotic  pressure  and  gas  pressure  both  seem  to  be  due  to 
molecular  motion,  we  may  reason  that  the  process  of  osmosis  is  prac- 
tically identical  with  that  of  the  passage  of  hydrogen  through  palladium. 

*  For  a  review  of  the  important  theories  as  to  the  cause  of  osmotic  pressure,  see 
article  by  Lovelace,  Am.  Chem.  Jour.,  39,  546  (1908).  It  may  be  remarked  here 
that  there  are  serious  objections  to  any  of  the  theories  proposed,  but  the  one  described 
above  seems  to  be  as  free  from  them  as  any. 

f  This  experiment  was  carried  out  by  Sir  William  Ramsay;  it  gave  results  within 
90-97  per  cent  of  the  theoretical.  See  Phil.  Mag.,  38,  206. 


FIG.  28. — Pfeffer's  os" 
motic  pressure  ap" 
paratus. 


162      FREEZING-POINTS  AND  BOILING-POINTS  OF  SOLUTIONS 


We  have  the  solution  on  one  side  of  the  membrane  and  the  pure  solvent 
on  the  other.  Evidently  the  concentration  of  the  solvent  molecules  is 
greater  on  the  side  where  there  is  no  solute;  and  if  it  is  soluble  in  the 
membrane  it  will  pass  through  it,  as  did  the  hydrogen  through  the 
palladium,  until  its  own  concentration  is  the  same  on  both  sides.  The 
partial  pressure  of  the  solute  will  then  make  itself  evident,  and  will  be 
exactly  measured  by  the  rise  of  the  manometer. 

Van't  Hoff's  Generalization. — If  the  explanation  we  give  above  is 
the  correct  one,  we  should  expect  to  see  a  very  close  relationship  between 
gas  pressure  and  osmotic  pressure.  If  Pfeffer  saw  in  his  results  any 
evidence  of  such  relationship  he  did  not  point  it  out,  and  so  it  remained 
for  the  great  Dutch  chemist,  Van't  HofT,*  to  do  so.  The  following  are 
some  of  Pf effer's  results  with  sugar  solutions : 

C  represents  the  concentration  in  grams  per  100  cc.  of  solution  and  P 
the  osmotic  pressure  in  centimeters  of  mercury. 


C. 

P. 

PIC. 

1 

53.5 

53.5 

2 

101.6 

50.8 

4 

208.2 

52.1 

6 

307.5 

51.3 

Observing  these  results,  Van't  Hoff  pointed  out  that  the  ratios 
obtained  in  the  third  column  above  were  really  a  demonstration  that 
Boyle's  law  holds  for  osmotic  pressure,  as  well  as  for  gas  pressure. 
P/C  is  a  constant,  and  since  the  concentration  of  any  solution  is  the 
reciprocal  of  the  volume,  we  may  substitute  1/V  for  C,  whereupon 
P/C  becomes  P/l/V.  Since  P/1/V  =  PV,  we  may  write  PV=& 
constant.  This  is  at  once  seen  to.be  the  primary  assumption  of  Boyle's 
law. 

Pfeffer  had  noticed  also  that  the  osmotic  pressure  of  any  given  solu- 
tion varied  with  the  temperature,  but  van't  Hoff  showed  that  the  vari- 
ation was  exactly  proportional  to  the  absolute  temperature;  in  other 
words,  that  osmotic  pressure  "  obeyed  "  Charles'  law.  Thus,  a  certain 
solution  gave  an  osmotic  pressure  of  51  cm.  at  14.2°  C.,  and  54.4  cm. 
at  32°  C.  The  absolute  temperatures  here  are  287.2°  and  305°,  respect- 
ively. To  make  the  pressures  exactly  proportional  to  these  would 

*  Jacobus  H.  Van't  Hoff  (1852-1911),  Professor  of  Physical  Chemistry,  Uni- 
versity of  Berlin.  Renowned  for  his  great  contributions  to  the  Theory  of  Solutions. 
His  paper  referred  to  was  in  Zeitschr.  physikal.  Chemie,  1,  481  (1887).  For  sketch 
of  his  life  see  Harrow,  "  Eminent  Chemists  of  Our  Time,"  p.  79. 


RECENT  WORK  ON   OSMOTIC   PRESSURE 


163 


require  that  the  second  should  be  54.6  cm.  instead  of  54.4  cm.     The 
agreement,  therefore,  is  almost  perfect. 

But  the  more  important  question  is,  whether  dissolved  particles 
have  the  same  kinetic  energy  as  gaseous  particles,  and  therefore  permit 
the  application  of  Avogadro's  law  to  solutions  as  well  as  to  gases. 
Again,  Van't  Hoff  found  in  Pfeffer's  values  an  experimental  answer  to 
this  question.  Pfeffer  had  determined  the  osmotic  pressure  of  a  1  per 
cent  solution  of  cane  sugar  at  different  temperatures,  and  Van't  Hoff's 
problem  was  to  determine  whether  this  osmotic  pressure  was  the  same 
as  the  pressure  of  a  gas  at  the  same  concentration  and  temperature. 
The  molecular  weight  of  cane  sugar  (CwHasOii)  is  342.  A  1  per  cent 
solution  (10  gm.  per  liter),  is  therefore  10/342  molar.  Van't  Hoff,  there- 
fore, calculated  the  gas  pressure  of  hydrogen  whose  concentration  was 
10/342  molar;  that  is,  10/342  of  2  gm.  per  liter.  These  pressures  he 
then  placed  alongside  the  corresponding  osmotic  pressures  of  the  sugar- 
solution  for  the  different  temperatures.  The  following  are  the  results: 


Temperature. 

Osmotic  Pressure 
in  Atmosphere. 

Gas  Pressure 
In  Atmosphere. 

6.8, 

0.664 

0.665 

13.7 

0.691 

0.681 

14.2 

0.671 

0.682 

15.5 

0.684 

0.686 

22.0 

0.721 

0.701 

32.0 

0.716 

0.725 

36.0 

0.746 

0.735 

Van't  Hoff  then  states  his  generalization  in  the  following  words: 
"  The  osmotic  pressure  exerted  by  any  substance  in  solution  is  the  same 
as  it  would  exert  if  present  as  a  gas  in  the  same  volume  as  that  occupied 
by  the  solution,  provided  that  the  solution  is  so  dilute  that  the  volume 
occupied  by  the  solute  is  negligible  in  comparison  with  that  occupied 
by  the  solvent." 

Recent  Work  on  Osmotic  Pressure. — Since  the  time  of  Pfeffer  and 
Van't  Hoff  much  work  has  been  done  along  the  line  of  osmotic  pressure. 
By  far  the  most  accurate  of  this  work  has  been  that  of  Morse,*  Frazer, 
and  Holland  of  Johns  Hopkins  University.  Their  more  accurate 
results  confirm  in  general  Van't  Hoff's  conclusions,  but  show  that 

*  See  Am.  Chem.  Jour.,  41,  258,  and  earlier  papers  mentioned  in  this  article. 
[Harmon  Northrop  Morse  (1848-1920),  Professor  of  Inorganic  and  Analytical 
Chemistry,  Johns  Hopkins  University.  1 


164       FREEZING-POINTS  AND  BOILING-POINTS  OF  SOLUTIONS 

osmotic  pressure  is  slightly  greater  in  most  cases  than  the  corresponding 
gas  pressure.  This  may,  of  course,  be  due  to  hydration,  as  explained 
under  Freezing-point  Depression.  » 

Osmotic  Pressure  and  Molecular  Weights. — If  Avogadro's  law  can 
be  applied  to  solutions  as  well  as  to  gases,  it  becomes  evident  at  once 
that  osmotic  pressure  may  serve  as  a  means  of  determining  molecular 
weights.  In  terms  of  osmotic  pressure  a  mole  is  that  weight  of  substance 
which  when  dissolved  in  22.4  liters  at  0°  C.  exerts  an  osmotic  pressure 
of  one  atmosphere.  The  work  done  at  the  Johns  Hopkins  University 
seems  to  indicate  that  this  would  be  more  accurately  stated  as  the 
weight  dissolved  in  22.4  liters  of  water.  This  really  amounts  to  the 
application  of  Van  der  Waals'  "  free  volume  "  principle  to  solutions. 
The  22.4  liters  of  water  would  correspond  to  the  free  volume,  V  —  6; 
the  total  volume  would  be  somewhat  greater.  Even  with  this  correc- 
tion, the  values  for  very  concentrated  solutions  still  deviate  considerably 
from  the  theoretical  values,  as  we  should  expect  when  we  consider  the 
great  concentration  of  solutions  as  compared  with  gases.  Thus,  a  molar 
solution,  which  is  not  considered  very  concentrated,  contains  1  mole  in  1 
liter,  while  a  gas  at  atmospheric  pressure  contains  only  1/22.4  mole  in  1 
liter.  We  should,  therefore,  have  to  put  a  gas  under  a  pressure  of  22.4 
atmospheres  to  make  it  as  concentrated  as  a  molar  solution.  Under 
this  pressure  many  gases  would  deviate  widely  from  the  gas  laws, 

EXERCISES 

1.  Give  some  common  examples  of  freezing-point  depression  caused  by  salts. 
What  is  the  cryohydric  point? 

2.  Give  the  kinetic  explanation  of  freezing-point  depression. 

3.  Explain  freezing-point  depression  by  use  of  the  vapor  pressure  curves  for 
water,  ice,  and  solution. 

4.  Explain  the  theory  of  molecular  lowering.     Give  the  molecular  lowering  of 
several  solvents. 

6.  Show  how  molecular  weights  may  be  determined  from  freezing-point  depres- 
sion. 

6.  What  depression  of  the  freezing-point  will  be  caused  by  dissolving  10  gm.  of 
bromine  in  1000  gm.  of  water? 

7.  If  3.25  gm.  of  a  substance  are  dissolved  in  80  gm.  of  benzene  the  freezing-point 
is  depressed  4.6°.     What  is  the  molecular  weight  of  the  substance? 

8.  What  is  the  freezing-point  constant  of  a  solvent  whose,  freezing-point  is 
depressed  3°  when  40  gm.  of  ethyl  alcohol  (C2H5OH)  are  dissolved  in  800  gm.? 

9.  Who  developed  the  theory  and  technique  of  freezing-point  and  boiling-point 
methods? 

10.  What  is  osmotic  pressure?     What  is  necessary  for  its  measurement? 

11.  Who  first  perfected  the  ferrocyanide  membrane?     Describe  his  method  of 
measuring  osmotic  pressure. 

12.  Give  the  kinetic  explanation  of  osmotic  pressure. 


EXERCISES  165 

13.  Give  data  showing  the  application  of  the  gas  laws  to  osmotic  pressure. 

14.  Give  Van't  Kofi's  generalization  regarding  osmotic  pressure  and  gas  pressure. 

15.  What  does  the  work  done  at  Johns  Hopkins  University  show  as  to  the  rela- 
tion between  osmotic  and  gas  pressure? 

16.  Define  molecular  weight  in  terms  of  osmotic  pressure,  applying  the  "  free 
volume  "  principle. 


CHAPTER    XIV 
THE  THEORY  OF  IONIZATION 

Historical  Development. — About  the  year  1800  it  became  known 
that,  when  a  current  of  electricity  was  sent  through  water,  hydrogen  and 
oxygen  gases  were  separated  at  the  respective  electrodes.  The  question 
arose  as  to  whether  the  atoms  of  these  gases  appearing  at  the  elec- 
trodes came  from  the  same  or  from  different  molecules  of  water.  It 
was  thought  possible  by  some  that  molecules  of  water  midway  between 
the  electrodes  might  be  decomposed,  and  that  the  atoms  of  the  two 
gases  might  then  travel  to  the  electrodes  and  appear  there  in  gaseous 
form.  Sir  Humphry  Davy  *  attempted  to  settle  this  question  by 
placing  the  electrodes  in  separate  beakers  of  water  and  then  connecting 
them  by  placing  a  finger  of  one  hand  in  one  beaker  and  a  finger  of  the 
other  hand  in  the  other.  He  found  that  the  gases  separated  at  the 
electrodes  as  usual  and  therefore  concluded  that  the  atoms  constituting 
them  came  from  different  molecules  of  water  (correct  conclusion,  but 
wrong  premise). 

In  1805  Grotthus  f  advanced  the  theory  that  the  atoms  of  oxygen 
and  hydrogen  are  all  firmly  bound  together  until  a  current  is  passed, 
and  that,  when  this  takes  place  a  molecule  of  water  nextHhe  negative 
electrode  separates  into  positively  charged  hydrogen  and  negatively 
charged  oxygen.  The  hydrogen  passes  to  the  electrode,  gives  up  its 
charge  and  escapes  as  hydrogen  gas.  At  the  same  time  the  oxygen  is 
repelled,  and  being  now  free,  combines  with  the  hydrogen  of  the  next 
molecule,  setting  another  oxygen  atom  free.  This  process  of  displace- 
ment continues  on  down  the  line  until  the  positive  pole  is  reached,  when 
the  oxygen  last  set  free  discharges  and  passes  off  as  oxygen  gas.  The 
distinctive  feature  of  this  theory  is  that  before  a  current  is  passed  there 
is  no  dissociation  at  all,  and  that  before  electrolysis  can  occur  work  must 
be  done  to  separate  the  atoms  from  each  other. 

About  1832  Faraday  J  carried  out  his  epoch-making  researches  on 

*  Sir  Humphry  Davy  (1778-1829),  Professor  of  Chemistry  at  the  Royal  In- 
stitution, London.  President  of  the  Royal  Society;  great  investigator  in  electro- 
chemistry. Isolated  the  alkali  metals;  invented  the  safety  lamp ;  proved  elementary 
nature  of  chlorine  and  iodine. 

t  Annalen  der  Chemie  (1),  68,  54  (1806). 

j  Expr.  Researches,  III,  Ser.  No.  373  (1832).  See  also  Thorpe's  Essays,  p.  185. 

166 


HISTORICAL  DEVELOPMENT  167 

electrolysis.  Besides  establishing  many  of  the  facts  of  electrolysis  in 
common  use  to-day,  he  gave  us  our  present  nomenclature.  Thus,  the 
products  appearing  at  the  electrodes  and  apparently  moving  through 
the  solution,  he  called  "  ions."  The  ion  separating  at  the  positive 
electrode  he  called  the  "  anion,"  meaning  "  to  go  up  ";  that  separating 
at  the  negative  electrode  he  called  "  cation/'  "  to  go  down."  The 
corresponding  electrodes  he  called  "  anode  "  and  "  cathode."  The  con- 
ducting substance  he  called  an  "  electrolyte."  It  should  be  remem- 
bered that  despite  his  use  of  the  term  "  ion,"  Faraday  had  no  clear 
conception  of  ionization  as  we  now  use  that  term;  his  names  apply  to 
the  products  of  electrolysis,  not  to  the  mechanism  of  conductance. 

In  1856  Clausius  *  showed  that  Grotthus'  theory  could  not  explain 
all  the  facts.  He  showed  that  if  the  part  molecules  were  combined 
rigidly  to  form  whole  molecules  a  certain  definite  potential  would  have 
to  be  reached  before  any  electrolysis  at  all  could  occur.  The  fact  was 
that  the  smallest  potential  produced  a  current  and  that  the  intensity  of 
this  current  increased  according  to  Ohm's  law.  He  therefore  con- 
cluded that  an  electrolyte,  while  consisting  mainly  of  whole  molecules, 
contained  also  some  part  molecules.  He  believed  that  in  an  elec- 
trolyte there  was  a  constant  interchange  of  part  molecules,  whether  a 
current  was  passing  or  not.  In  the  process  of  this  interchange  there 
must  necessarily  be  at  any  moment  some  free  part  molecules;  and  these, 
he  thought,  were  responsible  for  the  conductance  of  the  current.  Under 
such  conditions  no  E.M.F.  would  be  required  to  break  up  the  molecules, 
and  the  least  potential  would  cause  the  passage  of  a  current.  The 
work  of  the  current  would  be  simply  to  direct  the  course  of  the  part 
molecules,  which  were  already  free  and  oppositely  charged. 

Between  the  years  1853  and  1859  Hittorf  f  carried  out  his  researches 
on  the  movements  of  ions  in  solution.  He  showed  that  the  ions,  or 
part  molecules,  of  an  electrolyte  move  independently  through  the 
solution,  and  that  the  rates  of  motion  of  different  ions  are  not  neces- 
sarily the  same.  Nevertheless,  even  this  investigator  was  thinking  in 
terms  of  Clausius'  theory,  not  in  terms  of  our  modern  theory  of  ioniza- 
tion, which,  we  shall  see,  is  somewhat  different. 

About  the  year  1869,  Kohlrausch  J  invented  a  method  for  measuring 
the  resistance  offered  to  the  passage  of  a  current  through  an  electro- 

*  Poggendorff's  Annalen  101,  338,  (1857).  [Rudolph  Clausius  (1828-1888), 
Professor  of  Physics,  University  of  Bonn,  Germany.] 

t  tiber  die  Wanderungen  der  lonen."  Oswald's  Klassiker,  221,  p.  22.  [Johann 
Wilhelm  Hittorf  (1824-1914),  Professor  of  Physics,  University  of  Minister.] 

t  Poggendorff's  Annalen,  138,  280  (1869),  and  other  papers.  [Friedrich  Wilhelm 
Kohlrausch  (1840-1910),  Professor  of  Physics,  University  of  Strassburg;  President 
German  Bureau  of  Standards.] 


168  THE  THEORY  OF  IONIZATION 

lyte.  He  showed  that  the  conductance  (conductivity)  of  different 
electrolytes  differed  widely,  and  that  for  any  given  electrolyte  it 
increased  with  dilution,  in  most  cases  finally  reaching  a  maximum. 

Thus  before  the  year  1880  chemists  were  acquainted  with  most  of  the 
facts  of  electrolysis;  they  had  the  theory  of  Clausius  to  account  for 
these  facts;  they  knew  that  the  ions  in  a  solution  moved  about,  some- 
times at  different  rates;  they  knew  that  the  conductivity  of  solutions 
increased  with  dilution,  finally  reaching  a  maximum.  Besides  this,  the 
freezing-point  and  the  boiling-point  methods  for  the  determination 
of  molecular  weights  were  in  use,  accurate  work  along  these  lines 
having  been  made  possible  largely  by  the  researches  of  Raoult  and 
Beckman;  and  Pfeffer's  splendid  work  on  osmotic  pressure  was  well 
known. 

With  all  these  facts  in  mind,  Van't  Hoff,  in  1887,  brought  out  his 
great  work  on  the  analogy  between  solutions  and  gases.  While  engaged 
upon  this  work  he  discovered  that  many  members  of  the  three  great 
chemical  groups — acids,  bases,  and  salts — seemed  to  act  as  exceptions  to 
the  general  rule.  Thus,  their  osmotic  pressure  was  greater  than  the 
gas  pressure  would  be  for  a  like  concentration,  and  they  caused  too  great 
a  depression  of  the  freezing-point  and  too  great  an  elevation  of  the  boiling- 
point.  Van't  Hoff  saw  the  discrepancy  which  existed  here  and  pointed 
it  out  clearly  in  the  following  words:  "  If  we  are  still  considering  ideal 
solutions,  a  class  of  phenomena  must  be  dealt  with  which,  from  the  now 
clearly  demonstrated  analogy  between  solutions  and  gases,  are  to  be 
classed  with  the  earlier  so-called  deviations  from  Avogadro's  law.  As 
the  pressure  of  the  vapor  of  ammonium  chloride,  for  example,  was  too 
great  in  terms  of  this  law,*  so  also  in  a  large  number  of  cases  the  osmotic 
pressure  is  abnormally  large;  and  in  the  first  case,  as  was  afterwards 
shown,  there  is  a  breaking  down  into  hydrochloric  acid  and  ammonia  ;f 
so  also  with  solutions  we  would  naturally  conjecture  that  in  such  cases,  a 
similar  decomposition  had  taken  place.  Yet  it  must  be  conceded  that 
anomalies  of  this  kind,  existing  in  solutions  are  much  more  numerous, 
and  appear  with  substances  which  it  is  difficult  to  assume  break  down  in 
the  usual  way.  Examples  in  aqueous  solutions  are  most  of  the  salts, 
the  strong  acids  and  the  strong  bases.  ...  It  may  then  have 
appeared  daring  to  give  Avogadro's  law  for  solutions  such  a  prominent 
place,  and  I  should  not  have  done  so  had  not  Arrhenius  pointed  out  to 
me  by  letter  the  probability  that  salts  and  analogous  substances  when 
in  solution  break  down  into  ions." 

In  this  last  sentence  we  have  the  connecting  link  between  the 

*  Kopp,  Liebig's  Annalen,  105,  390;   Kekule,  ibid.,  106,  143. 
f  Pebal,  find.,  123,  199. 


HISTORICAL  DEVELOPMENT  169 

generalization  reached  by  Van't  Hoff  and  the  modern  theory  of  elec- 
trolytic dissociation.  The  latter  we  owe  to  the  Swedish  physical  chem- 
ist Arrhenius,  whose  work  we  shall  now  describe. 

Arrhenius'  paper  appeared  in  the  same  volume  of  the  Zeitschrift 
fur  physikalische  Chemie  as  Van't  Hoff's  paper.*  He  was  very  much 
impressed  by  Van't  Hoff's  generalizations  and  still  more  by  the  excep- 
tions. This  can  best  be  seen  by  quoting  his  own  words:  "  In  a  paper 
submitted  to  the  Swedish  Academy  of  Sciences  on  the  14th  of  October, 
1885,  Van't  Hoff  proved  experimentally  as  well  as  theoretically  the  fol- 
lowing unusually  significant  generalization  of  Avogadro's  law:  The 
pressure  which  a  gas  exerts  at  a  given  temperature,  if  a  definite  number  of 
molecules  is  contained  in  a  definite  volume,  is  equal  to  the  osmotic 
pressure  which  is  produced  by  most  substances  under  the  same  condi- 
ditions  if  they  are  dissolved  in  any  given  liquid. 

"  Van't  Hoff  has  proved  this  law  in  a  manner  which  scarcely  leaves 
any  doubt  as  to  its  correctness.  But  a  difficulty  which  still  remains 
to  be  overcome  is  that  the  law  in  question  holds  only  for  '  most  sub- 
stances,' a  very  considerable  number  of  aqueous  solutions  investigated 
furnishing  exceptions;  and  in  the  sense  that  they  exert  a  much 
greater  osmotic  pressure  than  would  be  required  from  the  law  re- 
ferred to. 

"  If  a  gas  shows  such  a  deviation  from  the  law  of  Avogadro  it  is 
explained  by  assuming  that  the  gas  is  in  a  state  of  dissociation.  The 
conduct  of  chlorine,  bromine  and  iodine  at  higher  temperatures  is  a  very 
well-known  example. 

"  The  same  expedient  may,  of  course,  be  made  use  of  to  explain  the 
exceptions  to  Van't  Hoff's  law;  but  it  has  not  been  put  forward  up  to 
the  present  probably  on  account  of  the  newness  of  the  subject,  the  many 
exceptions  known,  and  the  vigorous  objections  which  would  be  raised 
from  the  chemical  side  to  such  an  explanation." 

Arrhenius  then  sets  forth  his  theory  and  shows  how  all  the  excep- 
tions to  Van't  Hoff's  law  are  explained  by  it.  For  example,  osmotic 
pressure  is  proportional  to  the  number  of  particles  present  in  a  given 
volume  of  solution.  If  a  substance  exerts  an  abnormally  great  osmotic 
pressure  there  must  be  more  particles  present  than  we  should  expect 
from  the  concentration.  But,  applying  Avogadro's  law  to  solutions, 
we  must  admit  that  equimolar  concentration  means  also  an  equal 

*  Zeitschr.  physikal.  Chemie,  1,  631  (1887).  [Svante  August  Arrhenius  (1859-  ) 
Director  of  the  Laboratory  of  Physical  Chemistry,  Nobel  Institute,  Stockholm,  j 
For  sketch  'of  Arrhenius'  life  see  Harrow,  "  Eminent  Chemists  of  Our  Time,' 
p.  111.  See  also  Willard  Gibbs  Address  by  Arrhenius,  Jour.  Am.  Chem.  Soc., 
34,  353. 


170  THE  THEORY  OF  IONIZATION 

number  of  molecules  in  an  equal  volume.  That  is,  a  tenth  molar  solu- 
t'on  of  sodium  chloride  would  contain  the  same  number  of  molecules 
per  cubic  centimeter  as  a  tenth  molar  solution  of  cane  sugar.  If,  there- 
fore, the  osmotic  pressure  of  the  sodium  chloride  solution  is  1.83  times 
as  great  as  that  of  the  sugar  solution,  we  must  assume  that  the  sodium 
chloride  solution  contains  1.83  times  as  many  particles  per  cubic  centi- 
meter as  does  the  sugar  solution.  This  can  be  explained  by  assuming 
that  83  per  cent  of  the  sodium  chloride  molecules  are  split  up  into  the 
ions  Na+  and  Cl~. 

Arrhenius  thus  goes  back  to  the  theory  of  Clausius,  which  had  been 
advanced  thirty  years  before,  but  he  adds  to  this  theory  one  new  and 
all-important  feature;  he  shows  how  it  becomes  possible  to  calculate 
what  proportion  of  the  molecules  of  a  substance  are  in  the  ionic  condi- 
tion. He  thus  transforms  what  was  a  merely  qualitative  suggestion 
into  a  definite  theory  which  can  be  tested  by  experiment. 

He  then  goes  on  to  show  how  the  degree  of  ionization  can  be  calcu- 
lated from  conductivity  and  from  freezing-point  measurements,  and 
shows  that  the  values  calculated  by  these  two  methods  agree  very  closely. 
This  he  regards  as  the  crucial  test. 

lonizable  Substances  and  their  Ions. — As  mentioned  above,  the  only 
substances  which  ionize  to  any  appreciable  extent  are  acids,  bases,  and 
salts,  and  there  are  many  substances  which  belong  in  one  or  another  of 
these  classes  and  do  not  ionize  appreciably.  Thus,  such  acids  as 
palmitic,  stearic,  and  boric  ionize  very  little;  and  such  bases  as  the 
alcohols  and  the  hydroxides,  of  silicon  and  aluminum  scarcely  ionize 
at  all.  Practically  all  salts,  except  a  few  mercury  salts,  ionize  quite 
largely.  This  is  a  point  of  distinction  which  should  be  remembered. 
Even  a  salt  made  by  union  of  a  non-ionizing  acid  and  an  ionizing  base 
or  vice  versa,  will  almost  invariably  ionize  freely.  Some  of  the  most 
important  reactions  in  solution  are  the  result  of  this  fact.  Acetic  acid, 
hydrosulphuric  acid  (H2S),  hydrocyanic  acid,  and  ammonium  hydroxide, 
for  example,  ionize  very  little,  but  sodium  acetate,  sodium  sulphide, 
sodium  cyanide,  and  ammonium  chloride  ionize  as  freely  as  any  other 
salts. 

The  positive  ion  of  an  acid  is  always  hydrogen,  and  the  negative  ion 
is  the  radical  characteristic  of  the  given  acid.  Thus  hydrochloric  acid 
ionizes  according  to  the  equation : 

HC1<=»H+  + Gl- 
and sulphuric  according  to  the  equation: 


WHY  SUBSTANCES   DO   OR   DO   NOT  IONIZE  171 

Sulphuric  acid  may  also,  under  certain  conditions,  ionize  so  as  to  give  the 
univalent  bisulphate  ion,  thus: 

H2S04^±H++HSO4- 

All  polybasic  acids  may  ionize  in  a  similar  way. 

The  positive  ion  of  a  base  is  usually  a  metal,  the  negative  ion  is 
always  hydroxyl.  Where  the  positive  ion  is  not  a  metal  it  is  a  positive 
group  acting  in  the  same  capacity,  e.g.,  NH4+.  The  following  will 
serve  as  examples  of  basic  ionization: 

NaOH«=iNa++OH- 
and 

NH4OH<=±NH4++OH- 

The  positive  ion  of  a  salt  is  the  same  as  that  of  a  base,  and  the  nega- 
tive ion  the  same  as  that  of  an  acid.  Thus  the  salt  K2SO4  ionizes  so  as 
to  give  the  positive  ion  of  KOH,  and  the  negative  ion  of  H2SO4.  A 
double  salt  may  give  two  positive  ions,  thus : 

KA1(SO4)2  gives  both  K+  and  Al+++  as  positive  ions. 

Some  substances  ionize  either  as  bases  or  as  acids,  depending  on 
the  environment.  Such  substances  are  called  "  amphoteric."  Thus, 
aluminum  hydroxide,  when  in  the  presence  of  a  strong  acid,  ionizes  as  a 
base,  and  when- in  the  presence  of  a  strong  base  it  ionizes  as  an  acid.  We 
shall  take  up  these  amphoteric  substances  again  in  a  later  section. 

Why  Substances  do  or  do  not  Ionize. — The  reason  why  ionization 
is  confined  to  the  substances  we  call  acids,  bases,  and  salts  is  probably  to  be 
found  in  the  kind  of  combination  which  binds  the  atoms  together. 
In  our  chapter  on  Atomic  Structure  we  noted  two  possible  kinds  of  com- 
bination; one  involving  the  transference  of  electrons  from  one  atom  to 
another,  the  other  involving  no  transference  but  a  sharing  of  electrons 
between  atoms.  We  showed  also  that  transference  always  resulted 
in  a  polar  compound,  the  parts  of  which  (the  ions)  were  only  loosely 
held  together.  Sharing,  we  showed,  resulted  in  a  non-polar  compound, 
having  strong  interatomic  unions.  In  ionizable  acids  we  undoubtedly 
have  polar  combination  between  the  hydrogen  and  the  acid  radical, 
resulting,  when  the  acid  is  in  solution,  in  a  more  or  less  complete  separa- 
tion of  the  hydrogen  from  the  rest  of  the  acid.  In  bases  we  have  to 
assume  polar  combination  between  the  metal  and  the  hydroxyl  group. 
Inside  the  acid  radicals,  as  for  example,  C2H302~,  or  S04=,  we  must 
assume  that  only  a  sharing  of  electrons  occurs.  Otherwise  we  should 
expect  sulfuric  acid  to  give  oxygen  and  sulphur  ions  as  well  as  hydrogen 


172  THE  THEORY  OF  IONIZATION 

ions,  and  we  should  expect  all  the  hydrogen  in  acetic  acid  to  ionize,  not 
simply  one  atom.  Acetic  acid  would  also  give  carbon  and  oxygen  ions. 
Since  substances  like  sugar  give  no  ions  at  all  we  must  assume  in  these 
cases  that  all  the  atoms  are  combined  by  the  sharing  process. 

Our  theory  explains  rather  easily  also  the  fact  that  certain  salts  ionize 
freely  when  the  acids  or  bases  from  which  they  are  derived  do  not.  Hydrogen 
contains  one  lone  electron  which  it  is  loath  to  give  up;  it  much  prefers 
to  go  into  partnership  with  some  other  atom  where  it  can  "  pair  off  " 
its  electron  with  another  electron.  Metals  like  sodium  contain  a  lone 
electron  in  the  outer  shell  far  removed  from  the  nucleus,  and  they  are 
only  too  glad  to  part  with  it  if  opportunity  offers.  This  difference 
explains  why  sodium  acetate  is  freely  ionized  while  acetic  acid  is  not: 
sodium  allows  the  transference  of  its  electron,  resulting  in  polar  com- 
bination; hydrogen  does  not.  The  fact  that  acetic  acid  is  slightly 
ionized  may  be  accounted  for  by  supposing  that  under  some  compelling 
outside  influence  (from  the  solvent,  for  example)  a  few  of  the  molecules 
which  are  very  favorably  situated  may  show  polar  combination  of  the 
hydrogen. 

Charges  Carried  by  the  Ions. — As  can  at  once  be  seen  from  the 
above  discussion,  the  charge  carried  by  an  ion  is  due  to  the  presence  or 
absence  of  one  or  more  electrons.  The  magnitude  of  the  charge  will  be, 
then,  either  the  same  as  that  of  an  electron  (4.77  X10~10  electrostatic 
units)  or  some  multiple  of  this.  The  sodium  ion,  Na+,  carries  one  pos- 
itive charge  of  this  magnitude,  because  it  has  given  up  an  electron;  a 
chloride  ion,  Cl~,  carries  one  negative  charge  of  this  magnitude  because 
it  has  taken  on  an  extra  electron.  The  magnesium  ion,  Mg++,  carries 
two  positive  charges  of  electronic  magnitude  because  it  has  given  up 
two  electrons. 

Function  of  the  Solvent  in  lonization. — It  is  a  well-known  fact  that 
the  evidences  of  ionization  exist  in  water  solution  in  a  much  more  marked 
degree  than  in  most  other  solvents;  and,  knowing  that  water  is  more 
strongly  dielectric  than  most  other  liquids,  J.  J.  Thomson  *  and  Nernst  f 
suggested  that  the  ionizing  power  of  all  solvents  was  in  some  way  con- 
nected with  their  dielectric  nature.  Recently,  Walden  J  has  shown 
that  there  really  does  exist  a  close  proportionality  between  ionizing 
power  and  dielectric. 

*  Phil.  Mag.  (5),  36,  320  (1893). 

fZeitschr.  physikal.  Chemie,  13,  531,  (1893).  [Walther  Nernst  (1864-  ), 
Professor  of  Physical.  Chemistry,  University  of  Berlin.] 

JZeitschr.  physikal  Chemie,  54,  129,  (1906);  30,  1074.  [Paul  Walden  (1863- 
),  Professor  of  Physical  Chemistry,  Polyclinic  Institute,  Riga,  Russia];  see  also 
McCoy,  Jour.  Am,  Chem,  Soc,,  30,  1074. 


FUNCTION  OF  THE  SOLVENT  IN  IONIZATION  173 

Before  going  further  we  should  explain  what  we  mean  by  dielectric. 
Faraday  discovered  in  1837  that  the  attraction  or  repulsion  between 
two  electric  charges  depended  not  alone  on  the  size  of  the  charges  and 
their  distance  from  each  other,  but  also  on  the  nature  of  the  inter- 
vening medium.  Two  charges  which  attract  each  other  with  a  certain 
force  when  air  intervenes  will  possess  only  one-eightieth  of  this  attrac- 
tion when  water  is  the  medium.  Dielectric  may  be  defined,  then,  as 
the  power  possessed  by  different  substances  of  rendering  electric  charges 
indifferent  to  each  other.  Water  possesses  eighty  times  as  much  power 
in  this  direction  as  does  air.  Therefore,  if  the  dielectric  of  air  is  called  1, 
that  of  water  is  evidently  80. 

That  there  should  be  a  proportionality  between  dielectric  and 
ionization  seems  quite  natural.  The  different  ions  of  a  substance  are 
oppositely  charged  particles,  and  they  should,  for  this  reason,  attract 
each  other.  If,  however,  they  in  some  way  become  separated  in  the 
presence  of  a  medium  of  high  dielectric,  their  power  to  recombine  should 
be  very  much  reduced.  The  greater  the  dielectric  of  the  solvent,  the 
greater  the  reduction  in  the  combining  power  of  the  ions,  in  other  words, 
the  greater  the  ionization. 

That  this  theory  is  borne  out  by  the  facts  can  be  seen  in  a  qualitative 
way  by  comparing  the  dielectrics  of  the  following  solvents  with  their 
ionizing  power: 

Solvent.  Dielectric. 

Water 81 

Methyl  alcohol 32 

Ethyl  alcohol 22 

Ammonia  (liquid) 22 

Chloroform 5 

Ether 4 

Benzene 2 

It  is  a  well-known  fact  that  water,  having  the  highest  dielectric,  is 
the  best  ionizer  of  all  these  solvents.  But  it  is  also  known  that  methyl 
alcohol  is  next,  followed  by  ethyl.  Ether  and  benzene,  with  low 
dielectrics,  are  very  poor  ionizers. 

But  Walden  has  shown  *  that  there  is  something  more  than  a  qual- 
itative proportionality  between  dielectric  and  ionizing  power;  he  has 
worked  out  a  quantitative  relation.  He  took  a  single  electrolyte 
(tetra-ethyl  ammonium  iodide),  which  could  be  dissolved  in  a  number  of 
different  solvents,  and  diluted  each  solution  until  the  degree  of  ionization 
was  the  same  in  all  cases.  He  then  found  that  the  product  obtained 

*  Zeitschr.  physikal.  Chemie,  64,  229. 


174 


THE   THEORY  OF  IONIZATION 


by  multiplying  the  dielectric  of  the  solvent  by  the  cube  root  of  the  dilu- 
tion *  was  a  constant,  that  is 

eVV  =  K 

The  first  half  of  the  table  below  shows  the  values  Walden  obtained  for 
several  solvents  when  the  degree  of  ionization  was  made  47  per  cent, 
and  the  second  half  when  it  was  made  91  per  cent: 


Solvent. 

e. 

V. 

e>7V. 

Methyl  alcohol  

32 

8 

65 

Ethyl  alcohol 

21  7 

50 

80 

Benzaldehyde  

16.9 

69 

75 

Acetyl  bromide  

16.2 

100 

77 

Water 

80 

110 

383 

Nitro  methane  

40 

800 

371 

Furfurol  

39.4 

600 

365 

Methyl  cyanide 

36 

1000 

358 

Methyl  alcohol  

32.5 

2000 

365 

It  will  be  noted  that  these  quantitative  values  are  in  line  with  the 
qualitative  statement  above.  Thus,  the  solvents  are  arranged  in  the 
descending  order  of  their  dielectrics,  and  the  necessary  dilutions  are  in 
ascending  order.  This  means  that  a  solution  in  a  solvent  of  low  dielec- 
tric must  be  at  great  dilution  to  give  the  same  degree  of  ionization;  in 
other  words,  that  the  ionizing  power  is  poor. 

In  line  with  this  dielectric  theory  is  the  so-called  "  salt  effect." 
It  has  long  been  known  that  the  addition  of  certain  neutral  salts  to 
water  solutions  of  electrolytes  resulted  in  an  increased  ionization.  f 
In  terms  of  dielectrics  this  is  easily  explained.  Solid  salts  are  in  general 
more  strongly  dielectric  than  solid  water.  Thus,  the  constant  for  ice  is 
3,  while  that  for  solid  NaCl  is  6.5.  Now,  liquid  water  has  a  much 
higher  dielectric  than  ice;  and  from  the  above,  that  of  liquid  NaCl 
should  be  still  higher.  We  should  expect,  therefore,  that  solutions 
of  salts  would  show  a  higher  dielectric  than  water.  Smale,  %  working  in 
Nernst's  laboratory,  seems  to  have  proved  this  to  be  true.  The  salt 
effect,  therefore,  adds  credence  to  the  dielectric  explanation  of  ionization. 

*  By  "  dilution  "  is  meant  the  number  of  liters  required  to  contain  1  mole  of 
solute.  This  is  the  reciprocal  of  the  concentration. 

t  See  Szyszkowski,  Zeitschr.  Physikal.  Chemie,  58,  420  (1907)  and  Arrhenius, 
ibid.,  31,  197. 

t  Wied,  Ann.,  60,  625  (1897). 


DEGREE  OF  IONIZATION  175 

We  should  say,  however,  in  this  connection,  that  recent  work  seems  to 
show  that  what  we  call  "  salt  effect  "  may  be,  partly  at  least,  a  matter  of 
hydration.  What  we  mean  is  this:  if  the  addition  of  sodium  chloride 
to  a  solution  of  acetic  acid  increases  the  concentration  of  hydrogen  ion 
it  is  not  necessarily  due  to  a  greater  percentage  ionization;  the  salt 
may  have  taken  up  some  of  the  water  to  form  a  hydrated  sodium 
chloride,  like,  for  example,  NaCl  •  2H20.*  This  process  would  lower  the 
amount  of  solvent  water  and  thus  make  the  acetic  acid  more  concen- 
trated. Some  experiments  conducted  in  this  laboratory  f  seem  to  show 
that  salt  effect  may  be  due  partly  to  increase  in  ionization  and  partly  to 
hydration. 

Degree  of  Ionization. — By  "  degree  "  of  ionization  is  meant  the 
fraction  ionized.  Thus,  if  in  solution  half  of  a  certain  acid  is  ionized 
and  half  in  the  molecular  condition,  we  say  the  degree  of  ionization  is 
one-half.  Degree  of  ionization  is  scarcely  ever  stated,  however,  as  a 
common  fraction,  but  almost  invariably  as  a  decimal  or  a  per  cent. 
Thus,  the  above  degree  would  be  stated  as  0.5  or  50  per  cent.  (We 
might  note  in  passing  that  an  error  is  often  made  in  translating  values 
from  per  cents  to  decimals.  Note  that  1.32  per  cent  means  decimal 
0.0132,  and  0.57  per  cent  means  decimal  0.0057,  etc.) 

The  methods  of  measuring  the  degree  of  ionization  are  interesting,  but 
we  can  scarcely  do  more  than  mention  them  here.  We  have  already 
spoken  of  the  conductivity  method  of  Kohlrausch.  This  can  be 
explained  more  clearly  in  the  chapter  on  Electrochemistry.  In  general, 
the  method  is  as  follows :  The  substance  is  taken  in  solution  in  a  certain 
known  concentration,  and  placed  in  a  conductivity  cell.  The  resistance 
to  the  passage  of  the  current  is  then  measured  in  ohms.  The  con- 
ductivity is  the  reciprocal  of  this  resistance.  The  solution  is  then 
diluted  with  an  equal  volume  of  water  and  the  total  conductivity  again 
determined.  It  is  found  to  increase  because  more  of  the  substance 
is  ionized.  The  process  is  then  repeated  again  and  again  until  a  point  is 
reached  where  further  dilution  causes  no  further  increase  in  conductivity. 
The  substance  is  then  understood  to  be  completely  ionized.  Now,  the 
conductivity  is  due  entirely  to  the  ions,  and  is  therefore  exactly  propor- 
tional in  any  case  to  the  degree  ol  ionization.  Where  the  conductivity 
is  at  its  maximum  the  substance  is  all  ionized;  where  the  conductivity 
is  half  as  great  the  ionization  is  50  per  cent,  etc.  In  general,  then,  the 
degree  of  ionization  may  be  determined  by  dividing  the  conductivity  at 

*  The  ions  of  the  salt  are  also  hydrated,  giving  such  compounds  as  Na+H2O. 
For  the  degree  of  hydration  of  certain  ions  and  for  methods  of  determining,  see  Wash- 
burn,  Jour.  Am.  Chem.  Soc.,  31,  322,  and  Smith,  ibid.,  37,  722. 

t  Master's  Thesis  by  H.  W.  Baker  (1920). 


176  THE   THEORY  OF  IONIZATION 

any  given  concentration  by  the  maximum  conductivity.  An  example 
will  make  this  perfectly  clear.  The  conductivity  of  M/10  acetic  acid 
at  18°  C.  is  4.67  reciprocal  ohms.  The  conductivity  of  acetic  acid  when 
completely  ionized  (the  maximum  conductivity)  is  347  reciprocal  ohms. 
The  degree  of  ionization  of  the  M/10  acid  is,  therefore,  4.67/347,  or 
0.0134,  equivalent  to  1.34  per  cent. 

Another  method  of  determining  degree  of  ionization  is  the  osmotic 
pressure  method.  This  we  have  also  mentioned  in  passing.  We 
showed,  for  example,  that  if  the  osmotic  pressure  of  a  certain  sodium 
chloride  solution  was  1.83  times  as  great  as  the  gas  pressure  would  be 
at  the  same  concentration,  we  could  explain  the  seeming  discrepancy 
by  assuming  that  83  per  cent  of  the  molecules  were  ionized.  Ths  osmotic 
pressure  method  is  little  used  because  of  the  great  difficulty  encountered 
in  making  accurate  osmotic  pressure  measurements. 

A  third  method  of  determining  degree  of  ionization  is  the  freezing- 
point  method.  We  know  that  in  those  cases  where  there  is  no  ioniza- 
tion the  molecular  lowering  in  water  is  1.86°  C.  If  then,  we  have  a  solu- 
tion containing  1  mole  of  solute  in  1000  gm.  of  water  and  find  the 
molecular  lowering  to  be  greater  than  1.86°,  we  can  calculate  from  the 
excess  lowering  the  degree  of  ionization  of  the  solute.*  Since  this 
method  is  rather  largely  used,  we  shall  give  in  detail  the  calculation 
relating  the  freezing-point  lowering  to  the  degree  of  ionization:  Let  d 
equal  the  observed  molecular  lowering.  Let  n  equal  the  number  of  ions 
resulting  from  the  ionization  of  1  molecule  of  the  solute.  Let  a  equal 
the  degree  of  ionization  to  be  calculated.  Now  if  the  breaking  up  of 
1  molecule  produces  n  ions,  we  obtain  in  the  case  of  this  1  molecule 
n  —  1  particles  more  than  we  had  to  begin  with.  If  a  is  the  fraction  of 
molecules  ionized  the  total  number  of  particles  added  by  this  process  will 
be  a(n—  1);  and  if  1  (unity)  is  allowed  to  stand  for  the  number  of 
molecules  before  any  are  broken  up,  then  the  total  number  of  par- 
ticles present  will  be  l+a(n—  1).  Finally,  since  the  freezing-point 
lowering  is  proportional  to  the  number  of  particles  present,  no  matter 
what  their  size,  the  observed  lowering  will  be  related  to  the  true  molecu- 
lar lowering  (1.86°)  just  as  the  total  number  of  particles  is  related  to  the 
original  number.  This  may  be  expressed  thus: 

d:  1.86::l+a(n-l)  :  1 
From  this  we  obtain: 

d-1.86 


Assuming  that  hydrates  are  not  formed. 


DEGREE  OF  IONIZATION 


177 


The  fact  that  the  solution  we  are  using  may  not  be  of  molar  concen- 
tration does  not  hinder  the  use  of  the  method.  In  case  the  solution 
were  only  M/10  we  should  assume  we  were  getting  only  one-tenth  of 
the  molecular  lowering  for  the  solution  and  should,  therefore,  multiply 
the  observed  value  by  10.  A  similar  procedure  would  apply  for  any 
concentration. 

We  should  again  note  in  passing  that  the  values  obtained  for  the 
degree  of  ionization  by  the  different  methods  agree  closely.  This,  as 
was  stated  before,  Arrhenius  regarded  as  the  crucial  test.* 

The  following  tables  give  the  degree  of  ionization  of  a  considerable 
number  of  acids,  bases,  and  salts.  Where  necessary,  the  type  of  ioniza- 
tion is  indicated.  Thus  H.  H.  864  means  that  all  the  ionization  is 
assumed  to  be  into  the  three  ions,  H+,  H+,  and  SC>4=.  H.  HSO*" 
means  that  all  the  ionization  is  assumed  to  be  of  the  primary  type,  giv- 
ing only  the  two  ions  H+  and  HSC>4~. 

It  will  be  noted  that  the  degree  of  ionization  of  acids  is  extremely 
variable.  We  have,  for  example,  nitric  and  hydrochloric  acids  with 
a  very  high  degree  of  ionization  on  the  one  hand,  and  such  acids  as  boric 
and  hydrocyanic  with  a  very  low  degree  on  the  other.  The  activity  of 
an  acid,  as  such,  has  been  found  to  be  directly  proportional  to  the  degree 
of  ionization,  indicating  that  hydrogen  ion,  and  not  the  molecular  acid, 

Degree  of  Ionization  of  Adds. 


HNO3,  N/10 0.92 

HNO3,  N 0.82 

HNO3  cone.  15  N 0.09 

HC1,  N/10 0.92 

HC1,  N 0.78 

HC1,  cone.,  12  N 0.13 

H2S04,  N/10,  H-H-SO, 0.61 

H2SO4,  N,  H-H-SO4 0.51 

H2SO4,  cone.,  18  M,  H-HSO4. ...  0.007 

HBr,  N/2 0.90 

HI,  N/2 0.90 

HC1O4,  N/2 0.88 


HC1O3,  N/2 0.88 

H2C204,  M/10,  H-HC204 0.50 

H3PO4,  M/10,  H-H2PO4 0.27 

H3PO4,  M,  H-H2PO4 0. 10 

HF-N/10 0.15 

H2Tr,f  M/10,  H-HTr 0.082 

HC2H302,  N/10 0.0134 

HC2H3O2,  N 0.0042 

H2CO3,  M/10,  H-HC03 0.0017 

H2S,  M/10,  H-HS 0.0007 

H3BO3,  M/10,  H-H2BO3 0.0001 

HCN,  N/10 0.0001 


Degree  of  Ionization  of  Bases. 


KOH,  N/10 0.91 

KOH,  N 0.77 

NaOH,  N/10 0.91 

Ba(OH)2,  N/10 0.77 

LiOH,  N 0.63 

Ca(OH)2,  N/64 0.90 


NH4OH,  N/10 0.0134 

NH4OH,  N/2 0.0057 

N(CH3)4OH,  N/16 0.96 

Sr(OH)2,  N/64 0.93 

AgOH,  N/1783 0.39 

H2O,  H-OH  (at  20°  C.) 10~7 


*  See  also  A.  A.  Noyes,  Report  of  the  Congress  of  Arts  and  Sciences,  Vol.  IV, 
p.  311.     (St.  Louis,  1904.) 
f  Tartaric  acid. 


178 


THE   THEORY  OF  IONIZATION 


Degree  of  lonization  of  Salts. 
(All  of  N/10  concentration  unless  otherwise  indicated). 


KOI.. 
KBr.  . 
KI.  .  . 
KNO3. 


0.86 
0.86 
0.86 
0.83 


NaHCO3 0.78 

Na2HPO4 0 . 73 

Na2Tr 0.69 

BaCl2 0.77 

CaSO4,  N/100 0.64 

CuSO4 0.39 

AgNO3,  N/10 0.81 

AgNOs,  N/20 0.85 

ZnSO4 0.40 

ZnCl2 0.73 

HgCl2,  approx 0.01 

Hg(NO3)2,  approx 0 . 10 

Hg(CN)2 Trace 

Cd(N03)2,  N 0.56 

CdBr2,N 0.16 


KC2H3O2 0.83 

K2SO4 0.72 

K2CO3 0.71 

KC1O3 -. 0.83 

NH4C1,  N 0.74 

NH4C1,  N/10 0.85 

NaCl,  N 0.66 

NaCl,  N/2 0.74 

NaCl,  N/10.  . 0.84 

NaNO3 0.83 

NaC2H3O2,  N/5 0.76 

NaC2H3O2,  N/10 0.79 

NaC2H302,  N/20 0.83 

Na2SO4 0.70 

is  the  important  factor.  Highly  ionized  acids  are  therefore  spoken  of 
as  "  strong,"  and  those  that  are  little  ionized,  as  "  weak."  According 
to  this  standard,  sulphuric  acid  is  much  weaker  than  hydrochloric,  and 
in  line  with  this  we  really  find  that  its  activity  is  less  in  every  way. 

Bases  also  show  considerable  variation  in  the  matter  of  strength. 

Salts  are  nearly  always  highly  ionized,  as  the  table  shows,  al- 
though the  terms  "  strong  "  and  "  weak  "  are  not  applied  to  them. 
Some  of  the  salts  of  mercury  and  cadmium  are  about  the  only  exceptions. 

The  lonization  of  Water. — The  degree  of  ionization  of  water  is  given 
in  the  table  as  10~7  at  20°  C.  This  means  that  out  of  a  liter  of  water 
the  small  fraction  of  a  mole  represented  by  this  number  is  in  the  ionic 
condition,  giving  H+  and  OH~  ions.  It  will  be  noted  in  this  connection 
that,  since  each  molecule  of  water  ionized  gives  one  H+  ion  and  one  OH~ 
ion,  a  liter  of  pure  water  at  20°  C.  will  contain  10~7  moles  of  H+  ion 
and  10~7  moles  of  OH~  ion;  in  other  words  the  concentration  of  each 
of  the  ions  in  pure  water  at  20°  C.  is  10~7.  A  surprising  thing  about  this 
ionization  of  water  is  that  in  any  water  solution,  at  20°,  the  product  of  the 
concentration  of  the  two  ions,  H+  and  OH~,  is  10~14.  In  pure  water, 
for  example,  or  any  neutral  solution,  the  product  is  10~7XlO~7,  or 
10~14.  In  an  acid  solution  the  concentration  of  the  H+  ion  will,  of 
course,  be  large,  but  that  of  the  OH~  will  be  correspondingly  small,  so 
that  the  product  is  still  10~14.  In  a  basic  solution  we  have  the  opposite 
condition,  that  is,  the  OH~  ion  concentration  is  large  and  H+  ion  con- 
cent ration  is  small;  but  here  again  the  product  of  the  two  will  be  10~14. 
Why  this  is  so  we  cannot  discuss  here,  but  we  shall  do  so  when  we  take 


IONIC   CONCENTRATION  179 

up  the  subject  of  equilibrium.     It  is  sufficient  for  us  here  simply  to 
state  the  fact. 

Ionic  Concentration. — One  of  the  most  common  uses  for  the  ioniza- 
tion  values,  such  as  are  given  in  the  above  table,  is  in  determining  the 
molar  concentration  of  the  ions  in  a  given  solution.  The  idea  seems 
simple,  but  few  calculations  seem  to  confuse  the  average  student  more 
than  this  one.  For  this  reason  we  shall  try  to  clear  up  the  method  by 
use  of  a  few  illustrations : 

(1)  What  is  the  concentration  of  Na+  ion  in  N/10  solution  of  NaCl? 

Since  NaCl  is  univalent,  N/10  means  also  M/10.  In  other  words  the 
total  molar  concentration  is  0.1.  According  to  the  table  above,  N/10 
NaCl  is  0.84  ionized.  From  this  we  infer  that  0.84  of  the  total  con- 
centration is  in  the  ionic  condition.  This  gives  us  0.84  of  0.1,  or  0.084, 
as  the  concentration  of  the  ionic  NaCl.  But  each  molecule  of  ionic 
NaCl  gives  one  Na+  ion.  Therefore  the  concentration  of  Na+  ion  is 
also  0.084. 

(2)  What  is  the  molar  concentration  of  SO4=  ion  and  of  H+  ion,  in  N/10  H2SO4? 

Since  H2SO4  is  here  indicated  as  bivalent,  an  equivalent  weight  is 
1/2  the  molar  weight;  and  1/10  of  an  equivalent  weight,  as  we  have  it  in 
the  N/10  acid,  means  1/20  of  a  mole.  In  other  words,  N/10  H2SO4  is 
M/20  H2S04,  also  stated  as  0.05  M.  Now,  according  to  the  table, 
N/10  H2SO4  is  0.61  ionized.  This  means  that  0.61  of  the  whole  0.05 
mole  found  in  a  liter  is  ionic,  giving  for  the  concentration  of  the  ionic 
H2SO4,  0.61  of  0.05,  or  0.0305.  Each  molecule  of  ionic  H2S04  gives 
one  SO4=  ion.  Therefore,  the  concentration  of  the  S04=  ion  will  be 
the  same,  namely  0.0305.  But  each  molecule  of  ionic  H2SO4  gives  two 
H+  ions.  Therefore,  the  concentration  of  the  H+  ion  will  be  twice  the 
molar  concentration  of  the  ionic  H2S04  and  twice  that  of  the  SO4=  ion, 
namely  0.061. 

(3)  A  saturated  solution  of  Sr(OH)2  is  0.063  molar,  and  the  base,  at  this  dilution, 
is  90  per  cent  ionized.     Calculate  the  concentration  of  both  ions. 

The  molar  concentration  of  the  ionized  base  will  be  0.9  of  0.063,  or 
0.0567,  and  since  each  molecule  of  Sr(OH)2  contains  1  atom  of  Sr, 
the  concentration  of  the  Sr++  ion  will  be  the  same  as  that  of  the  ionized 
part,  namely  0.0567.  But  each  molecule  of  Sr(OH)2  gives  two  OH 
groups.  Therefore,  the  concentration  of  the  OH~  ion  will  be  double 
that  of  the  ionized  part  as  a  whole  and  double  that  of  the  Sr++  ion, 
namely  0.1 134. 

If  it  is  desired  to  know  what  weight  of  an  ion  is  present  in  a  given 
solution,  it  is  necessary  first  to  calculate  its  concentration.  If  we  then 


180  THE   THEORY  OF  IONIZATION 

remember  that  concentration  means  "  moles  per  liter/'  we  should  be  able 
to  calculate  what  weight  of  ion  is  required  to  give  this  number  of  moles. 
This  will  be  the  weight  sought  for  if  the  volume  of  the  given  solution  is  1 
liter.  If  not,  the  true  weight  may  be  calculated  by  proportion.  Take 
the  following  example : 

What  weight  of  SO4=  ion  is  present  in  200  cc.  of  N/10  H2SO4? 

From  example  2  above,  we  see  that  the  concentration  of  the  S04= 
ion  in  N/10  H2SO4  is  0.0305.  The  weight  of  1  mole  of  SO4  is  32+64,  or 
96  gm.  and  that  of  0.0305  mole  would  be  0.0305X96  gm.,  or  2.928  gm. 
This  is  the  weight  of  S04=  ion  in  1  liter  of  N/10  H2SO4.  In  200  cc. 
there  will  be  1/5  of  2.928  gm.,  or  0.5856  gm. 

lonization  of  Polybasic  Acids. — As  previously  indicated,  polybasic 
acids  ionize  in  what  might  be  termed  "  steps."  Thus,  sulphuric  acid 
ionizes  first  into  H+  and  HSO4~,  and  the  latter  ion  then  ionizes  into 
H+  and  SO4=.  Carbonic  acid  ionizes  first  into  H+  and  HCOs",  and 
the  latter  ion  then  breaks  down  into  H+  and  C0s=.  Phosphoric  acid 
ionizes  in  three  steps,  first  into  H+  and  H2PO4~~,  next  into  H+  and 
HPO4=,  and  finally  into  H+  and  PO^ 

The  separation  of  the  first  hydrogen  ion  from  a  polybasic  acid  is 
called  "  primary  "  ionization,  the  separation  of  the  second  is  called 
"  secondary,"  and  the  separation  of  the  third,  "  tertiary."  This 
"  step  "  ionization  is  well  indicated  by  the  following  scheme  repre- 
senting the  ionization  of  phosphoric  acid: 

H3PO4  <=>  H++H2P04-  (primary) 

IT 

H++HP04=     (secondary) 

IT 

H++P04=     (tertiary) 

In  the  case  of  any  polybasic  acid  the  primary  ionization  always 
predominates,  and  in  concentrated  solution  constitutes  practically  all 
the  ionization.  Thus,  rather  concentrated  sulphuric  acid  contains 
practically  no  ions  except  H+  and  HS04~,  that  is,  no  S04=  ions  are 
present.  This  accounts  for  the  formation  of  acid  sulphates  like  KHSO4 
in  the  presence  of  concentrated  sulphuric  acid.  In  moderately  dilute 
solutions  of  polybasic  acids  secondary  ionization  may  become  pro- 
nounced, but  only  in  extremely  dilute  solutions  does  the  tertiary  have  a 
ponderable  value-. 

The  following  table  gives  the  degree  of  the  different  sorts  of  ioniza- 
tion of  several  polybasic  acids  in  M/10  solution,  it  being  understood 
that  in  any  case  all  the  sorts  are  occurring  simultaneously: 


IONIZATION   AND   CHEMICAL  ACTIVITY 


181 


Acid,  M/10. 

Primary. 

Secondary. 

Tertiary. 

Phosphoric                       .        

0  27 

2X10~6 

4X10~12 

Cs.rbon.ic 

0  0017 

7X10~10 

Sulphuric  
Hydrosulphuric 

0.38 
0  0007 

0.20 
1  2X10~14 

Oxolic 

0  50 

5X10~4 

tlonization  and  Chemical  Activity. — That  chemical  activity  is  pro- 
portional to  ionization  is  proved  at  every  turn.  We  shall  see  that 
practically  every  chemical  reaction  with  which  we  are  concerned  in 
analytical  chemistry  is  in  some  way  dependent  upon  the  degree  of 
ionization  of  the  reacting  substances.  If  this  were  not  true  the  evi- 
dences of  ionization  would  be  nothing  more  than  interesting  facts, 
and  we  should  not  have  been  justified  in  spending  so  much  time  in  devel- 
oping the  theory. 

We  could  multiply  the  number  of  examples  showing  the  relation 
between  ionization  and  chemical  activity,  but  we  have  room  for  only  a 
few: 

(1)  The  water  solution  of  hydrochloric  acid  conducts  the  current, 
gives  abnormal  osmotic  pressure  and  freezing-point,  affects  indicators, 
etc.     It  is,  therefore,  ionized;  and,  so  far  as  we  know,  all  the  properties 
of  its  water  solution  are  the  properties  of  H+  ion  and  Cl~  ion.     Thus, 
its  hydrogen  is  displaced  by  metals;  it  has  a  sour  taste;  it  precipitates 
silver  chloride.     On  the  other  hand,  dry  hydrogen  chloride,  either  as  gas 
or  liquid,  gives  the  normal  molecular  weight,  and  does  not  conduct. 
It  is,  therefore,  not  ionized.     Moreover,  it  has  none  of  the  properties 
of  an  acid;  e.g.,  it  does  not  attack  carbonates,  and  metallic  sodium  will 
remain  in  contact  with  the  gas  for  months  without  tarnishing.* 

(2)  Again,  a  solution  of  HC1  in  dry  benzene  or  toluene  gives  no  evi- 
dences of  ionization  ;f  neither  do  dry  powders  react  under  ordinary 
conditions.      For  example,  baking  powder,  a  mixture  of  dry  potassium 
bitartrate  and  sodium  bicarbonate,  remains  inactive  for  years,  so  long 
as  no  moisture  enters.     Fused  salts  do  react  on  each  other,  but  they  also 
conduct  well,  and  are  therefore  ionized.     A  common  example  is  the 
reaction  of  fused  sodium  carbonate  on  calcium  sulphate  according  to 
the  equation 

CaSO4+Na2CO3  ^  CaCO3+Na2SO4 


*Cohen,  Chem.  News,  54,  305  (1896). 

t  See  Baker,  Jour.  Chem.  Soc.,  66,  611,  and  73,  422,  also  Hughes,  Phil.  Mag., 
34,  117. 


182  THE   THEORY  OF  IONIZATION 

(3)  It  is  possible  that  in  some  cases  non-ionized  molecules  do  react. 
In  the  case  of  reactions  of  organic  substances  in  organic  solvents  it  has 
been  supposed  that  the  processes  are  non-ionic.     Possibly  the  ordinary 
slowness  of  such  reactions  is  due  to  this  fact.     It  is  more  likely,  how- 
ever, that  the  reactions  are  really  ionic  even  here,  and  that  the  extreme 
slowness  is  due  to  the  slightness  of  the  degree  of  ionization,  not  to  its 
entire  absence.*     Kahlenberg  f  has  shown,  too,  that  certain  reactions 
in  organic  solvents  occur  with  great  speed,  and  claims  to  have  shown  the 
complete  absence  of  any  evidences  of  ionization.     It  should  be  noted, 
however,  that  water  gives  only  very  slight  evidence  of  ionization,  and 
yet  certain  reactions  with  water  certainly  involve  the  ions  H+  and  OH~, 
and  are  at  the  same  time  almost  instantaneous.    The  great  speed  may  be 
due  to  the  enormous  mobility  of  the  ions,  which  in  a  measure  over- 
comes the  smallness  of  the  number.     Kahlenberg's  results  may,  there- 
fore, be  due,  not  to  the  interaction  of  non-ionized  molecules,  but  to  the 
interaction  of  ions,  few  in  number  but  of  great  speed,  t 

(4)  Another  fact  which  shows  well  the  relation  between  ionization 
and  chemical  activity  is  that  certain  well-known  and  very  delicate 
chemical  tests  fail  when  applied  to  certain  substances  known  to  contain 
the  element  or  group  tested  for.     This  we  explain  by  assuming  that 
the  given  element  or  group  is  not  in  the  ionic  condition,  or  is  so  slightly 
ionized  as  not  to  respond  to  the  test.     Thus,  iron  in  the  ferric  condition, 
usually  gives,  with  ammonium  thiocyanate,  blood-red  ferric  thiocyanate, 
and  with  sodium  hydroxide,  brown  ferric  hydroxide,  but  both  of  these 
tests  fail  when  applied  to  potassium  ferricyanide,  K3Fe(CN)6,  although 
this  salt  contains  ferric  iron.     This  is  easily  understood  when  we  con- 
sider that  the  iron  is  securely  locked  up  in  the  complex  ion  Fe(CN)e~, 
and  that  no  ferric  ion,  Fe+++,  exists.     Another  interesting  example  is 
potassium  ferric-oxalate,  K3Fe (€204)3,  which  gives  a  test  for  iron  with 
sodium  hydroxide,  but  not  with  the  thiocyanate.     The  iron  is  here  also 
locked  up  in  a  complex  Fe(C2O4)=,  but  not  so  securely  as  in  the 
above  case.     A  slight  amount  of  ferric  ion  still  exists,  sufficient  in 
amount  to  respond  to  the  delicate  hydroxide  test,  but  too  minute  to 
give  the  less  delicate  thiocyanate  test.     Silver  ion  is  used  as  a  test 
for  chloride  ion,  Cl~,  but  no  test  is  given  with  chloroform,  CHCls,  or 
with  potassium  chlorate,  KClOs,   in  the  first  case  because  there  is 
practically  no  ionization,  and  in  the  second  case  because  the  ion  formed 
is  C103-,  and  not  Cl~. 

*  Sunlight  increases  the  speed  of  certain  reactions,  notably  organic.  This  may  be 
due  to  the  ionizing  power  of  light.  See  Haber,  Zeitschr.  Elektrochemie,  11,  847. 

t  Jour.  Phys.  Chem.,  6,  1,  (1902). 

t  Haber,  loc.  cit.,  10,  433,  773.  See  also  Cady  and  Lichtenwalter,  Jour.  Am. 
Chem.  Soc.,  35,  1434. 


IONIZATION  AND  CHEMICAL   ACTIVITY  183 

(5)  As  another  example  of  the  relationship  between  ionization  and 
chemical  activity,  we  shall  mention  the  catalyzing  effect  which  the  dif- 
ferent acids  and  bases  have  upon  the  hydrolysis  of  an  ester.     Methyl 
acetate  reacts  with  water  to  form  methyl  alcohol  and  acetic  acid,  as 
represented  by  the  following  equation: 

CH3C2H3O2-f  H2O  <=±  CH3OH+HC2H3O2 

With  water  alone,  this  reaction  is  almost  immeasurably  slow,  but  in 
the  presence  of  hydrogen  or  hydroxyl  ion  it  is  hastened,  and  the  amount 
of  hastening  (the  catalysis)  is  exactly  proportional  to  the  concentration 
of  these  ions.*  Suppose  we  take  two  equal  portions,  say  5  cc.,  of  methyl 
acetate,  and  mix  them  at  the  same  moment  with  equal  portions  of  two 
acids,  say  sulphuric  and  hydrochloric,  of  the  same  normal  concentration. 
The  process  of  hydrolysis  will  begin  at  once,  and  its  speed  will  be  pro- 
portional to  the  concentration  of  the  hydrogen  ion.  If  the  degree  of 
ionization  is  the  same  in  the  two  cases,  the  rate  of  hydrolysis  will  be 
the  same ;  if  not,  the  speed  will  be  greater  in  one  case  than  in  the  other. 
In  order  to  find  out  what  the  speed  is  in  the  two  cases,  we  allow  the  reac- 
tion to  proceed  for  a  certain  time,  then  stop  it  by  adding  sufficient 
standard  alkali  to  exactly  neutralize  the  acid  added,  and  finally  titrate 
the  acetic  acid  set  free.  The  relative  amounts  of  acetic  acid  are  meas- 
ures of  the  relative  speeds  of  reaction  in  the  two  cases,  and  if  we  compare 
these  speeds  with  the  degree  of  ionization  of  the  two  acids,  we  shall  find 
them  proportional  to  the  latter. 

(6)  As  a  final  example  we  may  mention  the  remarkable  uniformity 
in  the  heat  of  neutralization  of  strong  acids  and  bases. 

It  has  been  found  that  when  one  equivalent  of  a  strong  acid  is  neu- 
tralized with  one  equivalent  of  a  strong  base  in  dilute  solution  a  constant 
amount  of  heat  is  developed.  This  fact  also  remained  unexplained  until 
the  theory  of  ionization  came  to  the  rescue.  In  terms  of  this  theory  it 
becomes  the  expected  thing.  Thus,  a  dilute  solution  of  hydrochloric 
acid  should,  according  to  the  theory  of  ionization,  contain  only  the  ions 
H+  and  Cl~,  while  a  dilute  solution  of  sodium  hydroxide  should  con- 
tain only  the  ions  Na+  and  OH~.  If  dilute  equimolar  solutions  of  these 
two  substances  were  mixed  we  should  expect  no  change  so  far  as  the 
Na+  and  Cl~  ions  are  concerned — they  would  simply  remain  ionic. 
But  we  notice  that  H+  and  OH~  are  the  ions  of  water,  and  we  know 
that  water  is  scarcely  at  all  ionized.  It  is  impossible  that  these  two 
ions  should  remain  uncombined  when  they  have  the  opportunity  to 
combine.  They  therefore  unite  to  form  undissociated  water,  and  in  so 

*  Arrhenius,  Zeitschr.  physikal.  Chemie,  2,  289. 


184  THE   THEORY  OF  lONI^ATION 

doing  set  free  a  certain  amount  of  heat.  Now,  our  theory  demands 
that  the  interaction  between  any  strong  acid  and  base  should  occur  in 
the  same  general  way,  that  is,  by  union  of  H+  and  OH~  only,  and  there- 
fore the  same  amount  of  heat  should  be  liberated  in  each  case,  provided, 
of  course,  that  the  solutions  are  dilute  and  that  the  same  number  of 
equivalents  of  acid  and  base  are  used. 

The  following  table  gives  the  heats  of  neutralization  of  several  strong 
r.cids  and  bases.  It  is  understood  that  in  each  case  the  amounts  react- 
ing are  one  equivalent  of  acid  and  one  equivalent  of  base. 

HC1    +NaOH 13,700cal. 

HBr    +NaOH 13,700  cal. 

HNOa+NaOH 13,700  cal. 

HI       +NaOH 13,800  cal. 

HC1     +KOH 13,700  cal. 

HC1    +L1OH 13,700  cal. 

HC1    +l/2Ba(OH)2 13,800  cal. 

HC1    +1/2  (Ca(OH)2 13,900  cal. 

We  are  justified,  then,  in  saying  that  the  interaction  between  strong 
acids  and  bases  in  dilute  solution  is  purely  ionic,  and  that  it  involves 
only  the  ions  of  water.  We  therefore  write  for  this  reaction  the  general 
onic  equation: 

H++OH-     -*H2O 

In  the  case  of  acids  and  bases  which  are  only  partially  ionized  even 
in  dilute  solution,  we  should  not  expect  to  find  the  regular  behavior 
above  described.  If,  for  example,  we  are  dealing  with  a  weak  acid  we 
should  expect  that  during  the  process  of  neutralization  the  small  amount 
of  hydrogen  ion  already  present  would  first  be  used  up,  and  that  more 
would  then  have  to  be  furnished  by  further  ionization  of  the  acid.  This 
process  should  either  liberate  or  consume  heat,  so  that  the  total  heat 
change  in  such  cases  would  be  more  or  less  than  13,700  cal.  The  fol- 
lowing values  prove  this  to  be  true. 

HC2H3O2  +NaOH 13,400  cal. 

l/3H3PO2+NaOH 14,830  cal. 

HF  +NaOH 16,270  cal. 

The  same  thing  is  true  also  of  the  neutralization  of  weak  bases,  as  the 
following  example  shows: 

HC1+NH4OH     12,300  cal. 


EXERCISES  185 


EXERCISES 

1.  Mention  the  steps  which  preceded  Arrhenius'  theory  and  the  men  prominently 
connected  with  them. 

2.  In  what  way  did  Arrhenius'  theory  differ  from  the  others? 

3.  What  substances  are  ionizable,  and  what  ions  do  they  give? 

4.  Show  how  the  two  types  of  combination  described  under  Langmuir's  theory 
may  be  responsible  for  the  ability  or  lack  of  ability  of  a  substance  to  ionize.     Exam- 
ples. 

6.  Explain  where  the  ions  get  their  electric  charges,  and  show  what  is  their  sign 
and  magnitude. 

6.  What  are  the  properties  of  Na  and  Na+,  of  Ag  and  Ag~*~,  of  H2  and  H+,  of  S 
and  S=,  of  I2  and  I~?     Write  the  formulas  of  substances  which  will  produce  the  ions 
indicated. 

7.  What  is  meant  by  "  dielectric"?     What  is  the  dielectric  constant  for  water? 
What  does  this  mean? 

8.  What  relation  exists  between  the  dielectric  and  the  ionizing  power  of  a  sol- 
vent? 

9.  WTiat  is  meant  by  "  salt  effect"?     How  related  to  dielectric? 

10.  How  may  hydration  enter  into  the  so-called  salt  effect? 

11.  What  is  meant  by  "  degree  of  ionization"?   Give  the  conductivity  method  of 
determining  this. 

12.  Develop  the  following  formula: 

d-l.SQ 
~1.86  (n-1)' 

13.  A  certain  salt  dissociates  into  three  ions,  and  the  degree  of  ionization  in  a 
solution  containing  1  mole  in  1000  gm.  of  water  is  0.33.     What  is  the  freezing-point 
depression  of  this  solution? 

14.  A  certain  salt  is  15  per  cent  ionized  in  a  solution  containing  1  mole  in  2000  gm. 
of  water,  and  the  F.  P.  depression  is  1.21°.     Into  how  many  ions  does  each  molecule 
dissociate? 

15.  Arrange  all  the  acids  given  in  the   ionization  table   in  the  order  of  their 
degrees  of  ionization. 

16.  What  salts  are  not  highly  ionized? 

17.  What  is  the  hydrogen  ion  concentration  in  N/10  acetic  acid?     In  N/10 
hydrogen  sulphide?     In  N/10  hydrochloric  acid?     In  N/10  sulphuric  acid? 

18.  What  is  the  molar  concentration  of  the  sulphate  ion  in  N/10  sulphuric  acid? 

19.  Calculate  the  molar  concentration  of  the  Hg++  and  of  the  NO3~  in  N/10 
mercuric  nitrate. 

20.  A  saturated  solution  of  magnesium  hydroxide  is  0.00015  molar.     If  the  base  is 
wholly  ionized  what  is  the  molar  concentration  of  the  magnesium  ion?     Of  the 
hydroxide  ion? 

21.  Calculate  the  OH~  concentration  in  N/10  solutions  of  ammonium  hydroxide 
and  sodium  hydroxide. 

22.  How  strong  a  solution  of  sodium  hydroxide  would  be  required  to  furnish  the 
same  OH~~  concentration  as  N/10  ammonium  hydroxide,  if  in  this  dilute  solution  the 
sodium  hydroxide  is  wholly  ionized? 

23.  The  degree  of  ionization  of  0.03  N  acetic  acid  is  2.45  per  cent.     What  weight 
of  each  ion  is  present  in  100  cc.  of  this  solution? 


186  THE   THEORY  OF  IONIZATION 

24.  Which  is  "  stronger,"  36  N  sulphuric  acid,  or  N  hydrochloric? 

25.  In  500  cc.  of  water,  0.85  gm.  of  calcium  hydroxide  is  dissolved  and  the  base  in 
this  solution  is  0.9  ionized.     Calculate  the  concentration  of  the  OH~  ion.     (The 
total  volume  of  the  solution  may  be  taken  as  500  cc.  without  appreciable  error.) 

26.  What  is  the  degree  of  ionization  of  pure  water  at  20°  C.?     What  are  the  con- 
centrations of  H+  and  OH~  in  pure  water  at  20°  C.?     What  is  the  product  of  the 
concentrations  of  these  two  ions  in  any  solution  at  20°  C.? 

27.  What  are  the  concentrations  of  H+  and  OH~  in  N/10  NaOH  and  in  N/10 
HC1,  both  at  20°  C.? 

28.  Discuss  the  ionization  of  polybasic  acids,  and  give  the  degrees  of  the  primary, 
secondary,  and  tertiary  ionization  of  molar  phosphoric  acid. 

29.  Give  several  examples  showing  the  effect  of  water  upon  chemical  activity. 
Explain. 

30.  Do  reactions  which  are  not  ionic  occur  in  solution?     Explain.     What  has 
Kahlenberg  to  say  about  this? 

31.  Explain  several   chemical  tests  which  are  dependent  on  the  presence   or 
absence  of  ionization. 

32.  Describe  in  detail  an  experiment  which  shows  how  the  rates  at  which  different 
acids  catalyze  the  hydrolysis  of  an  ester  are  related  to  their  degrees  of  ionization. 

33.  Explain  the  uniformity  found  in  the  heats  of  neutralization  of  strong  acids  and 
bases. 


CHAPTER  XV 
CHEMICAL  INDICATORS 

Nature  of  Indicators  and  their  Color  Changes. — Chemical  indicators 
are  organic  dyes  which  exist  in  two  so-called  "  tautomeric  "  forms,  the 
two  forms  possessing  different  colors.*  We  can  best  show  what  we 
mean  by  an  example :  Para  nitrophenol  is  a  compound  which  is  colorless 
in  an  acid  solution  and  orange  in  an  alkaline  solution.  In  an  acid  solu- 
tion the  molecule  has  the  structure  indicated  by  the  following  formula: 

C— OH 


When  the  solution  is  made  alkaline  with,  say  NaOH,  the  H  from 
the  OH  group  wanders  to  the  N02  group  and  changes  one  of  the  O's 
there  to  an  OH.  The  compound  then  has  the  following  structure: 

C=O 
HC/NCH 

(B) 


Sodium  or  some  other  metal  may  take  the  place  of  the  H  in  the  OH, 
giving  ONa,  for  example,  if  the  solution  is  concentrated  enough;  but, 
whether  it  does  or  not,  the  important  point  for  us  is  the  fact  that  form  A 
is  colorless  while  form  B  is  orange-colored. 

*Stieglitz,  Jour.  Am.  Chem.  Soc.,  26,  1112;  Acree,  Am.  Chem.  Jour.,  37,  71; 
39,  528,  649;  42,  115;  Ber.  9,  522. 

187 


188  CHEMICAL  INDICATORS 

Something  analogous  to  this  is  true  of  any  indicator:  it  exists  in  two 
forms,  and  these  two  forms  have  different  colors.  Methyl  orange,  for 
example,  takes  on  a  pink  form  in  acid  solution  and  a  yellow  form  in  basic 
solution.  Phenolphthalein  takes  on  a  colorless  form  in  acid  solution 
and  a  magenta  form  in  basic  solution. 

Relation  between  Color  Change  and  Concentration  of  H+  and  OH~. 
—We  have  shown  that  both  H+  and  OH~  are  present  in  any  solution,  an 
acid  solution  having  a  preponderance  of  H+  and  an  alkaline  solution  a 
preponderance  of  OH~.  We  have  shown,  too,  that  the  product  of  the 
concentrations  of  H+  and  OH~  is  a  constant  (10~14  at  20°  C.).  Now 
it  happens  that  in  the  case  of  all  the  useful  indicators  the  change  of  form 
(and  color)  is  dependent  in  a  very  sensitive  way  upon  the  ratio  between 
the  H+  and  OH~  concentrations.  Methyl  orange,  for  example,  stands 
just  at  the  verge  of  its  change  when  the  H+  concentration  is  10~4  and 
the  OH~  concentration  10~10,  or  very  nearly  that.  If  the  ratio  is 
changed  ever  so  little  towards  the  basic  side  by  increase  of  OH~  and 
decrease  of  H+,  the  indicator  instantly  begins  to  take  on  its  yellow  form 
and  lose  its  pink  color.  If  the  ratio  is  changed  towards  the  acid  side  by 
increase  of  H+  and  decrease  of  OH~,  the  opposite  change  begins  to 
take  place.  Either  change  can,  of  course,  be  noted  at  once  by  the  change 
in  tint.  Phenolphthalein  is  ready  for  its  change  of  form  when  the  H+ 
concentration  is  10~8  and  the  OH~  concentration  10~6.  A  slight  increase 
of  OH~  and  decrease  of  H+  changes  the  indicator  to  its  magenta  form; 
a  slight  increase  of  H+  gives  the  colorless  form. 

When  an  indicator  is  exactly  at  its  turning  point  we  have  to  assume 
that  part  of  the  molecules  are  in  one  form  and  part  in  the  other.  This 
is  often  evidenced  by  a  mixture  of  colors.  For  example,  when  methyl 
orange  is  at  its  turning  point  it  shows  a  mixture  of  pink  and  yellow, 
usually  spoken  of  as  a  salmon  tint.  The  turning  point  of  phenol- 
phthalein is  a  very  faint  pink,  a  mixture  of  magenta  and  white.  These 
turning  points  between  the  colors  of  indicators  are  spoken  of  as  their 
"  end  points." 

It  should  be  noted  that  the  end  points  of  indicators  are  not  neces- 
sarily coincident  with  the  neutral  point.  A  truly  neutral  solution,  as  we 
have  shown,  contains  H+  and  OH~  of  the  same  concentration,  namely 
10~7  (at  20°  C.).  Methyl  orange  is  therefore  seen  to  have  its  end  point 
in  a  slightly  acid  solution  and  phenolphthalein  in  a  slightly  alkaline 
solution.  This  is  a  very  important  point  to  remember,  for  it  is  a  rather 
common  fallacy  to  imagine  that  when  an  indicator  just  changes,  the 
solution  is  "  neutral/'  which  is  not  necessarily  the  case.  Litmus 
comes  very  near  indicating  a  truly  neutral  solution,  and  another  indi- 
cator (neutral  red)  takes  its  name  from  the  fact  that  it  does  this  exactly. 


RELATION  BETWEEN  COLOR  CHANGE  AND  CONCENTRATION      189 


The  fact  that  the  end  points  of  indicators  do  thus  vary  from  the  neutral 
point  makes  them  very  much  more  useful  than  they  would  otherwise  be. 
This  will  appear  as  we  proceed. 

The  following  table  gives  the  colors  exhibited  by  several  common 
indicators  in  alkaline  and  acid  solutions,  also  the  H+  and  OH~  concen- 
trations at  the  turning  points: 


Colors  Exhibited. 


End-point  Concentration. 


Indicators 

in  acid 

end  point 

in  alkali 

(H+) 

(OH-) 

Dimethylamino  azoben- 
zene 

decided 
pink 

salmon 

yellow 

4.9XH)-4 

2X10~U 

Methyl  orange 

pink 

salmon 

yellow 

2.1X10-4 

4.8X1Q-11 

Cochineal 

orange 

pink 

lilac 

1.7X10"4 

6X1Q-11 

Sodium  alizarin  sul- 
phonate 

brass- 
yellow 

brown 

cherry- 
red 

5.2X10"5 

1.9X1Q-10 

Congo  red 

blue 

violet 

red 

5.2X10"5 

1.9X10-10 

Alizarine 

brass- 
yellow 

old  rose 

pink 

3.7X10~5 

2.7X1Q-10 

Methyl  red 

violet  red 

pink 

yellow 

1.2X10"5 

8.5X10~10 

Azolitmin  (litmus) 

red 

violet 

blue 

10~6 

HT8 

Neutral  red 

magenta 

pink 

yellow 

10~7 

10~7 

Rosolic  acid 

yellow 

rose 

pink 

1.4X10"8 

7X10~7 

Phenolphthalein 

colorless 

pink 

magenta 

9.2X10"9 

1.1X1Q-6 

Thymolphthalein 

colorless 

sky  blue 

blue 

5.9X10-10 

1.7X10-5 

Trinitrobenzene 

colorless 

yellow 

orange 

10-ia 

10"1 

The  Color  Range. — We  have  already  noted  that  at  the  end  point  an 
indicator  exists  partly  in  one  tautomeric  form  and  partly  in  the  other. 
We  have  also  noted  that  any  change  in  the  H+/OH~  ratio  will  begin 

*  The  values  here  given  were  all  obtained  in  this  laboratory  by  use  of  the  hydrogen 
electrode,  except  those  for  litmus  and  trinitrobenzene.  See  also  Salm,  Zeitschr. 
physikal.  Chemie,  57,  471;  McCoy,  Am.  Chem.  Jour.,  31,  508;  A.  A.  Noyes,  Jour. 
Am.  Chem.  Soc.,  32,  815. 


190  CHEMICAL  INDICATORS 

to  throw  the  indicator  more  completely  over  into  one  or  the  other  of  its 
forms,  and  that  this  act  will  be  attended  by  a  change  in  color.  From 
this  it  is  evident  that  by  changing  the  ratio  sufficiently,  that  is,  by  making 
the  solution  strongly  enough  acid  or  alkaline,  an  indicator  can  be  thrown 
completely  over  into  one  of  its  forms.  Thus,  in  a  solution  whose  H+ 
concentration  is  10~3  and  whose  OH~  concentration  is  10~n,  methyl 
orange  will  exist  entirely  in  the  pink  form.  Further  addition  of  acid 
will  not  further  redden  the  indicator.  In  a  solution  whose  H+  con- 
centration is  5X  10~5  and  whose  OH~  concentration  is  2  X  10~10  this  indi- 
cator exists  only  in  the  yellow  form,  and  further  alkalinity  produces  no 
change.  Between  these  two  extremes  the  indicator  will  show  a  range 
of  tints  containing  varying  proportions  of  the  two  colors.  The  end- 
point  tint  is  usually  taken  as  something  near  the  mean  of  these  extremes. 

Considering  the  great  apparent  length  of  the  range  for  methyl  orange 
and  the  obvious  impossibility  of  always  selecting  exactly  the  same  tint 
in  titration  it  might  be  thought  that  great  inaccuracy  would  result. 
Let  us  see  if  this  is  so.  To  get  a  concentration  of  H+  ion  of  10~3  (0.001) 
requires  0.1  cc.  of  N-HC1  per  100  cc.  assuming  complete  ionization; 
and  to  get  a  concentration  of  5X10~5  requires  0.005  cc.  Thus  the 
whole  color  range  for  methyl  orange  is  compassed  by  the  very  small 
amount  of  0.095  cc.  of  N-HC1  in  100  cc.  of  solution.  Obviously,  it 
would  be  possible  to  select  a  tint  considerably  within  the  range,  so  that 
the  inaccuracy  from  this  source  need  certainly  not  be  greater  than  is 
measured  by  0.03  cc.  N-HC1.  In  practice  it  is  usually  less  than  this. 

The  color  ranges  for  different  indicators  vary  considerably;*  but 
for  those  used  in  analytical  work  it  is  always  short  enough  not  to  involve 
any  great  inaccuracy  except  in  the  hands  of  a  very  inexperienced  worker. 

Determination  of  End  Point  and  Range. — In  general  terms,  the 
method  of  determining  the  end  point  and  range  of  an  indicator  is  as 
follows : 

A  series  of  solutions  of  known  H+  and  OH~  concentration  is  pre- 
pared, reaching  all  the  way  from  rather  high  H+  and  low  OH~  concen- 
tration to  high  OH~  and  low  H+  concentration;  in  other  words,  from 
acid  to  basic.  These  solutions  are  placed  in  Nessler's  comparison  tubes 
on  a  suitable  rack,  and  a  small  uniform  amount  of  indicator  added  to 
each.  The  concentration  exhibiting  the  end-point  tint  can  then  be 
seen  at  once,  and  the  range  can  also  be  observed.  In  some  cases  the 
range  will  be  found  entirely  on  the  acid  side  (methyl  orange) ;  in  some, 
on  the  basic  side  (phenolphthalein) ;  and  in  others,  stretching  across 
the  neutral  point  (litmus). 

*  For  the  color  ranges  of  several  indicators  see  colored  insert  in  Clark's  "  Deter- 
mination of  Hydrogen  Ions,"  between  pp.  40  and  41. 


CHOICE  OF  AN  INDICATOR  191 

Choice  of  an  Indicator. — When  a  strong  base  like  NaOH  is  titrated 
with  a  strong  acid  like  HC1,  until  equivalent  amounts  of  the  two  solu- 
tions are  present,  the  resulting  solution  should  be  neutral.  In  such  a 
case  any  indicator  whose  end  point  is  not  too  far  from  the  neutral  point 
may  be  used. 

When  a  weak  acid,  like  acetic,  is  treated  with  a  strong  base  until 
equivalent  amounts  have  been  used,  the  resulting  salt  solution  is 
slightly  alkaline  because  of  hydrolysis,  and  in  such  a  case  an  indicator 
must  be  used  whose  end  point  comes  at  the  same  degree  of  alkalinity. 
The  point  is,  that  we  are  not  trying,  in  these  titrations,  to  get  a  neutral 
solution,  but  to  know  when  equivalent  amounts  of  acid  and  base  have  been 
used.  In  titrating  acetic  acid,  oxalic  acid,  benzoic  acid,  and  many  other 
organic  acids,  with  NaOH  phenolphthalein  is  the  indicator  used,  its  end 
point  coming  when  the  alkalinity  is  just  right.  If  methyl  orange  were 
used  in  these  cases  the  end  point  would  appear  before  an  equivalent 
amount  of  base  had  been  added.  Moreover,  the  end  point  would  not  be 
sharp  and  distinct.  In  other  words,  it  would  not  be  possible  to  tell 
just  when  the  end  point  was  reached. 

It  must  not  be  imagined,  however,  that  phenolphthalein  will  be 
satisfactory  as  an  indicator  for  every  weak  acid.  Some  acids  are  so 
weak  that  the  point  of  equivalence  between  acid  and  base  would  come 
where  the  alkalinity  was  too  great  for  phenolphthalein.  If  we  were  to 
use  phenolphthalein  in  such  cases  the  end  point  of  the  indicator  would 
appear  before  an  equivalent  amount  of  base  had  been  added,  just  as 
when  methyl  orange  is  used  with  a  moderately  weak  acid. 

When  a  weak  base  is  treated  with  an  equivalent  amount  of  a  strong 
acid,  the  salt  solution  formed  is  slightly  acid,  and  an  indicator  must  be 
chosen  which  gives  its  end  point  at  a  corresponding  acidity.  Thus,  in 
titrating  ammonium  hydroxide  with  a  strong  acid,  methyl  orange  or 
cochineal  will  work  perfectly.  Phenolphthalein  would  be  as  poor  an 
indicator  in  this  case  as  methyl  orange  would  be  in  the  case  of  a  weak 
acid. 

If  both  acid  and  base  are  weak,  and  equally  weak,  the  resulting  salt 
solution  should  be  neutral,  although  largely  hydrolyzed.  In  such  a 
case  the  same  indicator  would  apply  as  when  both  acid  and  base  are 
strong.  It  is  a  rare  thing,  however,  to  find  the  acid  and  base  equally 
weak;  therefore  the  use  of  indicators  in  such  cases  is  apt  to  be  very 
uncertain. 

Just  what  indicator  can  be  used  in  any  case  can  be  determined  by 
experiment.  If  an  indicator  gives  a  sharp  end  point  when  the  amount 
of  acid  and  base  are  equivalent,  it  is  a  perfectly  proper  indicator 
to  use. 


192  CHEMICAL  INDICATORS 

End-point  Correction. — We  have  said  that  when  a  strong  acid  is 
treated  with  an  equivalent  amount  of  a  strong  base  the  resulting  salt 
solution  should  be  neutral.  Thus  NaOH  and  HC1  give  a  neutral  solu- 
tion of  NaCl  when  mixed  in  exactly  equivalent  amounts.  If  in  the 
titration  of  NaOH  with  HC1  we  use  methyl  orange  indicator,  it  is 
evident  that  we  shall  not  end  the  titration  when  the  solution  is  neutral, 
as  it  should  be,  but  when  a  slight  excess  of  acid  is  added.  This  is 
because  methyl  orange  gives  its  color  change  in  a  slightly  acid  solution. 
If,  then,  we  wish  to  know  just  how  much  acid  is  required  to  balance 
the  NaOH  and  make  the  solution  neutral,  we  must  deduct  the  excess 
added  between  the  neutral  point  and  the  methyl-orange  end  point,  that 
is,  the  amount  of  acid  required  to  raise  the  H+  ion  concentration  of  the 
solution  from  10~7  to  2X10~4.  This  obviously  depends  on  the  final 
volume  of  the  solution  in  which  the  acid  and  alkali  have  been  mixed 
and  also  on  the  concentration  of  the  acid  used.  If  the  final  volume  of 
the  solution  was  1000  cc.  and  the  acid  used  was  normal,  1  cc.  in  excess 
would  give  a  concentration  of  10~3,  and  0.2  cc.  would  give  the  end  point 
concentration,  2X  10~4.  If  the  acid  were  N/10,  2  cc.  would  be  required 
to  give  this  concentration  in  1000  cc.  In  100  cc.,  0.2  cc.  of  N/10  acid 
would  be  required. 

If,  then,  in  carrying  out  a  titration  of  sodium  hydroxide  with  N/10 
hydrochloric  acid,  we  use  41  cc.  of  acid,  and  the  final  volume  of  the 
solution  is  100  cc.,  we  deduct  0.2  cc.  as  the  end-point  correction,  leaving 
as  the  amount  of  acid  equivalent  to  the  base,  40.8  cc. 

The  end-point  correction  with  cochineal  is  practically  the  same  as 
that  for  methyl  orange,  but  for  the  indicators  whose  end  points,  in 
terms  of  H+  concentration,  are  some  multiple  of  10~5  or  10~6  the  cor- 
rection would  be  insignificant. 

For  indicators  whose  end  points  lie  on  the  alkaline  side  of  the  neutral 
point,  the  error  would  be  in  the  opposite  direction;  that  is,  the  amounts 
of  acid  added  would  be  less  than  sufficient  to  neutralize  all  the  base. 
It  will  be  noted,  however,  that  the  OH~  concentrations  for  such  indi- 
cators as  are  given  in  the  table  all  come  with  inlO~5,  except  trinitroben- 
zene,  which  is  not  commonly  used.  Corrections  on  this  side  are,  there- 
fore, not  commonly  made. 

As  a  matter  of  caution  we  must  repeat  what  we  said  at  the  begin- 
ning of  this  section,  namely,  that  end-point  corrections  are  attempted 
only  in  the  titration  of  strong  acids  with  strong  bases.  Corrections  in 
other  cases  would  involve  certain  data  which  would  not  ordinarily  be 
available. 

Titration  of  Polybasic  Acids. — One  of  the  most  valuable  applications 
of  the  data  concerning  the  varying  sensitiveness  of  indicators  to  H+ 


TITRATION    OF  POLYBASIC  ACIDS  193 

and  OH~  comes  In  the  titration  of  polybasic  acids.  Two  common 
examples  have  been  chosen  to  show  this:  phosphoric  acid  and  carbonic 
acid. 

As  we  have  noted  before,  phosphoric  acid  ionizes  in  three  steps,  which 
are  called  primary,  secondary,  and  tertiary.  This  we  have  indicated 
thus: 

H3PO4  ?=*  H++H2PO4-(primary) 

IT 

H++HP04=  (secondary) 

u 

H++P04=  (tertiary). 

The  primary  ionization  gives  a  concentration  of  hydrogen  ion  of  about 
0.1  in  molar  solution.  The  secondary  and  tertiary  ionizations  are  very 
much  smaller.  If  an  alkali  (NaOH)  is  added,  the  primary  hydrogen  is 
first  neutralized,  leaving  the  ion  H2PO4~.  When  the  primary  hydrogen 
is  all  thus  neutralized,  it  happens  that  the  secondary  ionization  produces 
a  hydrogen  ion  concentration  of  2X  10~4,*  just  sufficient  to  give  the  end- 
point  tint  with  methyl  orange.  Therefore,  when  phosphoric  acid  is 
titrated  with  NaOH,  and  methyl  orange  is  used  as  indicator,  the  acid 
acts  like  a  monobasic  acid,  allowing  the  titration  of  only  one  of  its  three 
hydrogen  equivalents. 

If  we  continue  the  titration  with  the  alkali  the  secondary  hydrogen 
is  neutralized,  and  when  the  process  is  completed  we  have  left  in  solu- 
tion mainly  the  ion  HPO4=,  whose  tertiary  ionization  gives  a  hydrogen 
ion  concentration  of  10~8.  This,  it  will  be  noted,  is  the  correct  con- 
centration for  the  end  point  of  phenolphthalein.  It  is  evident,  there- 
fore, that  with  phenolphthalein  indicator  phosphoric  acid  would  act 
like  a  dibasic  acid,  allowing  the  titration  of  two  equivalents. 

With  trinitrobenzene  even  the  tertiary  hydrogen  may  also  be  neu- 
tralized, making  phosphoric  acid  here  function  as  a  tribasic  acid,  and 
leaving  in  solution  mainly  the  ion  PO4=.  f 

Carbonic  acid  is  an  example  of  a  very  weak  dibasic  acid.     Indicating 
its  ionization  as  in  the  case  of  phosphoric  acid,  we  have: 
H2CO3  i=>  H++HC03-  (primary) 

IT 

H++CO3=  (secondary) 

*  The  concentrations  of  the  secondary  and  tertiary  hydrogen  are  somewhat 
affected  by  hydrolysis  of  the  salts  produced.  The  values  given,  however,  are  empir- 
ical, and  thus  include  this  effect. 

t  It  is  understood,  of  course,  that  sodium  ion,  or  some  other  metallic  ion,  has  been 
introduced  in  the  process  of  titration;  but  this  has  nothing  to  do  with  the  theory  of 
the  process.  At  the  end  of  the  first  step  the  solution  may  be  said  to  contain  the  salt 
NaH2PO4;  at  the  end  of  the  second,  Na3HP04;  and  at  the  end  of  the  third,  Na3PO4. 


194  CHEMICAL  INDICATORS 

The  primary  ionization  gives  in  M/10  solution  a  concentration  of 
hydrogen  ion  of  1.7X10"4,  which  is  a  little  less  than  sufficient  to  give 
the  end-point  tint  with  methyl  orange.  And,  since  solutions  of  carbonic 
acid  of  even  this  concentration  are  usually  not  encountered,  this  acid 
may  be  regarded  as  too  weak  to  affect  methyl  orange.  It  is  strong 
enough,  however,  to  keep  phenolphthalein  in  its  colorless  form.  If 
we  neutralize  this  primary  hydrogen  with  an  alkali  we  have  left  in  the 
solution  the  bicarbonate  ion,  HC03~.  The  ionization  of  this  (secondary) 
gives  the  correct  concentration  of  hydrogen  ion  to  produce  the  end-point 
tint  with  phenolphthalein.  This  may  be  seen  by  preparing  a  solution 
of  sodium  bicarbonate  and  adding  to  it  a  drop  of  phenolphthalein  indi- 
cator. The  solution  will  either  give  the  pink  color  of  the  end  point,  or  be 
ready  to  do  so  upon  addition  of  a  drop  of  normal  alkali. 

Trinitrobenzene  would  allow  us  to  add  another  equivalent  of  base  to 
the  bicarbonate  ion,  giving  thus  the  normal  carbonate  ion,  CO3=,  as  in 
Na2CO3. 

From  what  has  been  said  it  is  evident  that  a  solution  of  sodium 
carbonate  would  be  alkaline  to  both  methyl  orange  and  phenolphtha- 
lein. If  we  titrate  this  with  an  acid  we  shall  have  the  changes  men- 
tioned above  occurring  in  reverse  order.  We  shall  have  the  CO3=  ion 
gradually  combining  with  the  H+  ion  from  the  acid  to  form  HC03~, 
thus, 

CO3=+H+-*HCO3- 

When  this  change  is  completed  the  color  due  to  phenolphthalein  van- 
ishes. Notice  that  this  end  point  comes  when  the  two  equivalents  of 
carbonate  have  reacted  with  one  equivalent  of  acid  (H+).  If  we  now 
add  methyl  orange  and  continue  the  titration  the  pink  color  of  this 
indicator  will  not  appear  until  all  the  second  equivalent  is  titrated,  that 
is,  until  the  bicarbonate  ion  is  changed  to  carbonic  acid,  thus: 

HCO3-+H+-+H2CO3 

Understand  that  it  is  not  the  carbonic  acid  which  then  brings  the  indi- 
cator to  its  end-point  color,  for  this  acid  is  too  weak  to  do  this;  it  is  the 
slight  excess  of  strong  acid  used  in  the  titration  which  does  it. 

Note,  finally,  that  with  phenolphthalein,  sodium  carbonate  acts  like 
a  univalent,  or  mon-acid,  base,  while  with  methyl  orange  it  acts  like  a 
bivalent,  or  di-acid,  base. 

Since  sodium  carbonate  is  easily  obtained  pure  and  anhydrous,  it  is 
much  used  as  a  standard  in  testing  the  concentration  of  acids  used  in 
volumetric  work. 


EXERCISES  195 


EXERCISES 

1.  What  are  chemical  indicators?     Show  by  means  of  an  example  what  structural 
changes  attend  the  change  of  color. 

2.  What  relation  is  there  between  the  color  change  of  an  indicator  and    the 
H+/OH~  ratio?     Illustrate  with  methyl  orange  and  phenolphthalein. 

3.  What  is  the  condition  of  an  indicator  at  its  turning  point,  or  end  point? 

4.  How  are  the  end  points  of  indicators  related  to  the  neutral  point?     Examples. 
6.  What  is  meant  by  the  "  range  "  of  an  indicator?     Illustrate  with  methyl 

orange. 

6.  Discuss  the  matter  of  inaccuracy  involved  in  the  range  of  methyl  orange. 

7.  How  are  the  end  point  and  range  of  an  indicator  determined? 

8.  What  sort  of  an  indicator  may  be  used  in  titrating  a  strong  base  with  a  strong 
acid? 

9.  What  sort  of  an  indicator  may  be  used  in  the  titration  of  a  weak  acid  with  a 
strong  base?     Name  such  an   indicator.     Would  methyl  orange  be  satisfactory? 
May  the  indicator  you  have  named  be  used  with  any  weak  acid?     Why? 

10.  What  sort  of  an  indicator  is  necessary  in  the  titration  of  ammonium  hydroxide 
with  hydrochloric  acid?     Explain. 

11.  Is  the  object  of  a  titration  always  the  getting  of  a  neutral  solution?     Why? 
Is  it  ever? 

12.  Give  general  procedure  for  determining  the  right  indicator  in  any  case. 

13.  What  is  meant  by  "  end-point  correction  "  ?     With  what  indicators  and  in 
what  titrations  is  it  used? 

14.  Forty  cc.  of  a  certain  sodium  hydroxide  solution  were  diluted  to  500  cc.  and 
then  titrated  with  N/10  hydrochloric  acid.     It  required  44.1  cc.  of  the  acid  to  neu- 
tralize the  base  to  the  methyl  orange  end  point.     Calculate  (a)  the  number  of  cubic 
centimeters  of  acid  equivalent  to  40  cc.  of  base;  (6)  to  what  volume  1  liter  of  the  base 
must  be  diluted  to  make  it  exactly  N/10? 

15.  Write  equations  indicating  the  three  steps  in  the  ionization  of  phosphoric 
acid. 

16.  Show  in  detail  how  certain  indicators  may  be  applied  in  the  titration  of  phos- 
phoric acid. 

17.  Show  how  carbonic  acid  ionizes  and  how  certain  indicators  may  be  applied 
in  its  titration. 

18.  Trace  the  changes  occurring  when  an  acid  (H+  ion)  is  added  to  a  solution 
of  sodium  carbonate:  (a)  to  the  phenolphthalein  end  point,  (6)  to  the  methyl-orange 
end  point. 

19.  Twenty-six  cc.  of  sodium  carbonate  solution  required  42  cc.  of  N/10  HC1  to 
neutralize  to  the  phenolphthalein  end  point.      What  weight  of  Na2CO3  is  con- 
tained in  1  liter  of  the  solution?     How  many  cubic  centimeters  of  N/10  HC1  would 
have  been  required  to  neutralize  the  26  cc.  of  carbonate  solution  to  the  methyl- 
orange  end  point? 

20.  Suppose  you  wished  to  prepare  an  exactly  neutral  solution  of  sodium  chloride 
by  combining  the  proper  acid  and  base.     What  indicator  would  you  use? 


CHAPTER  XVI 
HOMOGENEOUS  EQUILIBRIUM 

Definitions. — In  the  preceding  discussions  we  have  often  met  with 
cases  where  we  recognized  the  presence  of  two  opposing  tendencies, 
which,  although  in  full  operation,  were  acting  at  equal  speeds,  and  were 
therefore  in  equilibrium.  Thus,  water  in  a  closed  bottle  only  partly 
full  is  in  equilibrium  with  its  vapor,  for  the  liquid  is  passing  into  the 
vapor  form  at  exactly  the  same  rate  as  the  vapor  is  passing  back  into  the 
liquid  form.  Among  chemical  reactions  also  we  often  meet  with  cases 
involving  opposing  tendencies  which,  if  left  to  themselves,  come  into 
equilibrium.  Examples  are:  (a)  the  dissociation  of  calcium  carbonate, 
CaCOs,  into  CaO  and  CO2  and  the  reunion  of  these  products,  thus: 

CaCO3^CaO+CO2 

(b)   the  dissociation  of  nitrogen  tetroxide,   N204,  into  NO2  and  its 
re-formation  from  these  products  as  represented  by  the  equation 


(c)  the  reaction  of  hydrochloric  acid  in  solution  upon  sodium  hydrogen 
sulphate,  NaHSCU,  to  form  sulphuric  acid  and  sodium  chloride,  and  the 
reaction  of  these  products  to  form  the  original  substances,  thus: 

HCl+NaHS04  <=»  H2SO4+NaCl 

Comparing  these  four  cases  of  equilibrium — the  physical  equilibrium 
of  water,  and  the  three  cases  of  chemical  equilibrium — we  note  that  the 
first  two  cases  involve  distinct  physical  bodies  which  can  be  separated 
mechanically.  Such  cases  of  equilibrium  are  called  "  heterogeneous." 
The  other  two  cases  constitute  systems  which  are  alike  through  and 
through,  from  which  distinct  bodies  cannot  be  thus  separated.  Equi- 
libria of  this  sort  are  called  "  homogeneous."  These  two  classes  will 
include  all  the  cases  of  equilibrium  known. 

It  will  be  our  task  in  this  chapter  to  study  cases  of  homogeneous 
equilibrium  only.  In  the  next  chapter  we  shall  study  heterogeneous 

196 


IMPORTANCE— KINETIC  EXPLANATION  197 

equilibrium,  and  in  the  chapter  following  that  we  shall  study  cases  which 
involve  both  classes  at  once. 

Importance. — The  first  application  of  the  laws  of  equilibrium  to 
chemical  reactions  was  made  by  Guldberg  and  Waage  *  in  1867.  Since 
then  the  application  of  these  laws  has  been  extended  into  every  branch 
of  chemistry,  and  now  no  well-trained  chemist  attempts  to  advance  in 
any  line  without  carefully  considering  the  possible  equilibrium  effects. 
We  are  thus  justified  in  giving  these  laws  a  most  prominent  place  in  this 
course. 

Kinetic  Explanation. — The  law  of  chemical  equilibrium  may  be 
explained  in  the  following  simple  terms :  Suppose  the  substances  A  and 
B  are  brought  into  contact,  either  as  gases  or  in  solution,  and  that  these 
substances  react  to  produce  C  and  D.  Suppose  also  that  C  and  D  are 
able  to  react  to  produce  A  and  B.  The  rate  at  which  either  pair  of 
substances  will  react  depends  on  the  number  of  chances  presented  to 
them  for  favorable  impact,  and  this  in  turn  depends  on  their  molecular 
concentration.  At  the  start,  C  and  D  do  not  exist;  therefore  A  and  B 
react  at  a  velocity  which  is  infinitely  greater  than  theirs.  But  as  the 
reaction  proceeds  the  concentration  of  C  and  D  increases,  and  their  rate 
of  reaction  thus  increases.  After  a  time  both  pairs  of  substances  will  be 
reacting  at  the  same  rate,  and  after  that  there  will  be  no  further  change 
in  concentration.  The  two  reactions  are  then  in  equilibrium,  as  we 
indicate  by  the  equation. 

A+B+±C+D 

Note  that  when  this  condition  of  equilibrium  is  reached,  the  two 
reactions  are  still  in  full  operation.  The  only  reason  the  reaction 
seems  to  be  at  a  standstill  is  that  the  amounts  of  the  reacting  sub- 
stances remain  constant. 

In  most  cases  the  condition  of  equilibrium  above  described  is 
reached  almost  instantly  after  the  reacting  substances  are  mixed.  Only 
occasionally  do  we  notice  a  measurable  time  interval. 

Now,  it  is  not  to  be  understood  that  when  equilibrium  is  reached  the 
amounts  of  A  and  B  are  necessarily  the  same  as  those  of  C  and  D. 
There  may  be  cases  where  they  are,  but  such  a  circumstance  must  be 
considered  merely  accidental,  and  would  mean  simply  that  the  reacting 
capacity  of  A  and  B  exactly  equaled  that  of  C  and  D.  The  things  which 
are  equal,  when  equilibrium  is  reached,  are  the  speeds  of  the  forward 
and  the  backward  reactions.  But,  with  respect  to  the  amounts  of  the 

*[Cato  M.  Guldberg  (1836-1902),  Professor  of  Mathematics,  University  of 
Christiania;  Peter  Waage  (1833-1900),  Professor  of  Chemistry,]  University  of 
Christiania.]  See  Ostwald's  Klassiker,  No.  104. 


198  HOMOGENEOUS  EQUILIBRIUM 

reacting  substances  when  equilibrium  is  reached,  one  relationship  does 
exist,  and  this  is  the  all-important  relationship  in  equilibrium,  viz., 
the  product  of  the  molar  concentration  of  A  and  B  bears  a  certain  ratio  to 
the  product  of  the  concentrations  of  C  and  D.  Just  what  this  ratio  is, 
depends  on  the  reacting  substances;  but  for  any  one  set  this  ratio  is 
invariable,  no  matter  what  the  concentration  of  the  substances  may  be, 
provided  only  that  we  maintain  some  definite  temperature.  In  math- 
ematical form  this  relationship  may  be  stated  thus: 

(A)X(B) 
(C)X(Z>) 

where  (A),*  etc.,  are  the  molar  concentrations,  and  K  is  a  definite 
number,  called  the  "  equilibrium  constant." 

Let  us  see  how  the  above  equation  is  derived.  First  take  the  for- 
ward reaction 

A+B-+C+D 

For  definite  concentrations  of  A  and  B  and  for  some  definite  tempera- 
ture, the  speed  of  this  reaction  will  be  perfectly  definite;  that  is,  a 
certain  number  of  moles  will  react  per  second  or  hour.  If  we  double 
the  concentration  of  A,  there  will  be  twice  as  many  opportunities  for 
impact  between  A  and  B,  and  the  speed  of  the  reaction  will  be  doubled. 
We  see,  then,  that  the  speed  is  proportional  to  the  concentration  of  A. 
If,  when  the  concentration  of  A  is  doubled  we  also  double  that  of  B, 
we  shall  again  double  the  speed  of  reaction,  making  it  four  times  as  great 
as  at  first.  Thus  we  see  that  the  speed  is  also  proportional  to  the 
concentration  of  B.  If,  then,  the  speed  is  proportional  to  the  con- 
centration of  both  (A)  and  (B),  it  is  also  proportional  to  their  product, 
(A)X(B). 

We  do  not  say  that  the  speed  of  the  reaction  in  moles  per  liter  is 
the  product  of  (A)  X  (B),  but  only  that  it  is  proportional  to  this  product. 
This  means  that  if  the  product  of  (A)  X  (B)  is  doubled,  the  speed  will 
be  doubled,  etc.  But  if  the  speed  is  proportional  to  the  product  of  (A) 
and  (B),  we  can  say  that  the  speed  is  equal  to  the  product  of  (A)  and 
(B)  multiplied  by  some  constant.  Suppose,  for  example,  the  con- 
centration of  A  and  B  are  both  taken  as  10,  and  that  under  these  con- 
ditions A  and  B  react  with  a  speed  of  5  moles  per  second.  Now,  10X10 
is  not  5,  but  lOXlOX^i  will  be  5,  if  K\  is  the  number  showing  the 
relation  between  100  and  5.  KI  will  evidently  be  0.05,  and  we  can 
write : 

10X10X0.05=5 
*  Frequently  designated  also  by  [A];  etc. 


KINETIC  EXPLANATION  199 

If  we  double  (A)  we  shall  also  double  the  speed,  making  it  10,  and 
then  we  must  write : 

20X10X0.05  =  10 

If,  with  (A)  as  20,  we  make  (B)  1,  we  shall  have  made  the  chances  of 
impact  ten  times  fewer,  and  so  reduced  the  speed  from  10  to  1.  We 
then  write: 

20X1X0.05  =  1 

Note,  then,  that  in  all  these  cases  K\  really  is  a  constant,  and  only 
serves  to  express  the  relationship  between  the  product  (A)X(B),  and 
the  speed  Si. 

This  speed  constant,  KI,  may  be  thought  of  also  in  a  slightly  dif- 
ferent way.  If  we  make  the  concentration  of  A  and  B  both  1,  KI  will 
have  the  same  numerical  value  as  the  speed,  Si.  KI  may,  therefore  be 
thought  of  as  the  speed  at  unit  concentration. 

For  the  forward  action  A-\-B  — »  C+D,  the  following  general  equa- 
tion may  now  be  written: 

(A)X(B)XKi=Sl 

which  means  that  the  speed  is  equal  to  the  product  of  the  concentrations 
of  the  reacting  substances  multiplied  by  the  speed  constant. 

By  an  exactly  identical  method,  we  can  also  prove  that  for  the  reverse 
reaction,  A  +  B+-C+D, 

(C)X(D)XK2  =  S2 

Now  when  equilibrium  is  established  we  know  that  Si  equals  82,  no 
matter  what  the  concentration  of  the  several  reacting  substances  may 
be.  If  this  is  true,  then  the  two  products,  equal  respectively  to  Si  and 
82 j  must  also  be  equal;  that  is, 

(A)  X  (B)  XKi=  (C)  X  (D)  X  K2 
and  from  this, 

(A)X(B)  _K2 
(C)X(D)~Ki 

But  the  ratio  between  two  constants  is,  of  course,  also  a  constant,  so 
we  may  write : 

(A)X(B) 


(C)X(D) 
and  this  is  our  original  postulate. 


K 


200  HOMOGENEOUS   EQUILIBRIUM 

For  a  reaction  having  the  form  A+2B  <E±  C+D,  the  mathematical 
form  of  the  equilibrium  equation  becomes, 

(A)X(B)2 

" 


This  may  be  explained  as  follows:  The  reaction  may  occur  in  two  steps: 
A  +  B-+AB,  and  then  AB+B-^C+D,  AB  being  an  intermediate 
compound.  The  speed  of  the  first  reaction  is  proportional  to  (A)  and 
also  to  (B),  therefore  to  (.A)  X  (B).  The  speed  of  the  second  reaction  is 
proportional  to  (AB)  and  to  (B),  and  therefore  to  (AB)X(B).  But 
since  the  speed  with  which  AB  is  formed  is  proportional  to  the  product 
(A)X(B),  its  concentration  (AB)  at  any  moment  is  also  proportional 
to  (A)X(B).  We  may,  therefore,  substitute  this  product  for  (AB) 
in  the  second  reaction.  Instead  of  (AB)  X  (B)}  we  shall  then  have  (A)  X 


For  a  reaction  having  the  form  A+3B  —  »,  we  must  use  the  third 
power  of  (B).  In  general,  we  must  always  raise  a  concentration  to  the 
power  whose  exponent  is  the  same  as  the  coefficient  of  the  molecule  in 
.the  chemical  equation. 

Determination  of  the  Constant.  —  The  following  example  will  show 
how  an  equilibrium  constant  is  actually  worked  out: 

If  hydrogen  and  iodine  are  placed  in  a  closed  tube  and  heated  say 
to  440°  C.,  they  will  combine  to  form  hydriodic  acid.  But  at  this 
temperature  hydriodic  acid  also  decomposes  into  hydrogen  and  iodine. 
These  two  tendencies  will,  therefore,  come  into  equilibrium  according  to 
the  equation 

(1) 

According  to  the  above  discussion,  the  constant  for  this  equilibrium 
should  be  obtained  by  substituting  the  values  for  the  concentrations  in 
the  equation 
™  (H2)X(I2) 

~~ 


and  then  solving  for  K.  (Note  that  (HI)  is  squared  because  it  occurs 
as  2HI  in  the  chemical  equation.  Show  what  two  steps  might  occur 
in  this  reaction,  and  then  work  out  the  mathematical  equation  given 
immediately  above.) 

Bodenstein  *   determined   several   different    concentrations   of   the 
reacting  substances  which  were  in  equilibrium  at  440°  C.,  and  then 

*  Zeitschr.  physikal.  Chemie,  22,  16.     [Max  Bodenstein  (1871-       ),  Professor  of 
Physical  Chemistry,  Technical  School,  Hanover,  Germany.] 


EFFECT  OF  TEMPERATURE  CHANGE  ON  EQUILIBRIUM       201 


worked  out  the  constant.     The  following  table  gives  some  of  his  data. 
Concentrations   are   given  in   moles,  as   usual.     The   bracketed   sym 
bols  are  to  be  read  "  concentration  of";  for  example,  (H2)  means  "  con- 
centration of  hydrogen."     The  values  for  K  are  to  be  worked  out  by  the 
student. 


(H2). 

(It). 

(HI). 

K 

3.17 

8.06 

34.72 

»  .7*3* 

0.91 

33.3 

39.01 

,7  16 

2.06 

13.4 

36.98 

,7*77 

The  constant  for  any  reaction  is  calculated  in  practically  the  same 
way  as  for  this  reaction.  If  possible,  we  first  determine  the  course  of  a 
reaction,  so  as  to  be  able  to  write  correctly  the  mathematical  equation 
corresponding  to  (2)  above.  That  is,  we  need  to  know  what  molecules 
enter  into  the  reaction,  and  whether  to  use  the  first  power,  the  second 
power,  or  some  higher  power.  We  next  have  to  determine  experi- 
mentally what  concentrations  of  the  reacting  substances  can  exist  in 
equilibrium.  We  can  then  substitute  values  and  work  out  the  value  for 
K.  If  we  cannot  find  out  beforehand  what  powers  of  the  concentrations 
to  use,  we  have  to  write  the  equation  in  different  ways  and  then  see, 
after  substituting  values,  whether  the  ratio  comes  out  a  constant.  If 
it  does  we  assume  that  we  must  have  written  the  equation  correctly. 
This,  by  the  way,  makes  it  possible  sometimes  to  correct  an  erroneous 
notion  as  to  the  course  of  a  reaction. 

Effect  of  Temperature  Change  on  Equilibrium. — Every  chemical 
reaction  either  produces  heat  or  absorbs  heat.  A  reaction  which 
produces  heat  will  be  favored  by  a  lowering  of  the  temperature,  that 
is,  by  giving  the  heat  a  place  to  go.  Thus  the  condensation  of  steam 
produces  heat ;  for  when  we  run  steam  through  a  condenser  it  heats  the 
water  in  the  cooling  jacket.  Obviously,  this  reaction  will  be  favored 
by  taking  the  heat  away  as  fast  as  possible,  that  is,  by  lowering  the  tem- 
perature of  the  water  in  the  jacket.  A  truly  chemical  example  of  this 
kind  is  the  union  of  H2  and  I2  to  produce  HI.  This  reaction  produces 
heat,  and  is  therefore  favored  by  a  lowering  of  the  temperature.  Thus, 
below  440°  C.  these  two  substances  unite  more  completely  than  they  do 
above  440°. 

A  reaction  which  absorbs  heat  is  favored  by  a  rise  in  the  tempera- 
ture. A  physical  example  is  the  vaporization  of  water.  We  know,  of 
course,  that  this  reaction  absorbs  heat,  and  it  is  for  this  reason  that  our 


202  HOMOGENEOUS  EQUILIBRIUM 

hands  feel  cold  when  they  are  wet.  We  know,  too,  that  the  vaporization 
is  hastened  by  a  rise  in  the  temperature  of  the  water.  A  chemical 
example  of  this  kind  is  the  dissociation  of  HI  into  H2  and  12.  This 
reaction  absorbs  heat  and  is  therefore  favored  by  a  rise  in  temperature. 
This  means  that  at  temperatures  above  440°  C.  HI  dissociates  more 
completely  than  at  lower  temperatures. 

From  what  has  been  said  it  can  be  seen  that  change  in  temperature 
will  in  any  case  be  attended  by  the  shifting  of  equilibrium,  so  as  to  make 
the  value  of  the  constant  larger  or  smaller.  If  in  the  case  of  hydriodic 
acid,  for  example,  the  temperature  were  raised  above  440°,  dissociation 
into  H2  and  12  would  be  more  complete  and  the  value  for  K  would 
become  larger.  If,  on  the  other  hand,  the  temperature  were  lowered 
sufficiently,  H2  and  12  would  unite  almost  completely  and  the  value  for 
K  would  become  vanishingly  small.  In  any  case  the  application  of 
heat  will  cause  an  equilibrium  to  shift  in  such  a  direction  that 
heat  can  be  absorbed,  and  the  abstraction  of  heat  will  cause  it  to  shift 
in  the  opposite  direction.* 

Effect  of  Changes  in  Total  Pressure  on  Equilibrium. — Whether 
change  in  total  pressure  causes  a  shifting  of  an  equilibrium  depends  on 
whether  or  not  the  reaction  concerned  involves  a  change  in  volume. 
In  the  reaction 

H2+I2  <=*  2HI 

1  volume  H2  unites  with  1  volume  I2  (gas)  to  form  2  volumes  HI. 
Evidently  there  is  no  change  in  volume  here,  for  there  are  2  volumes  on 
either  side  of  the  equation.  Change  in  total  pressure  will,  therefore, 
not  affect  this  reaction;  for  any  shifting  in  either  direction  would  be 
attended  by  as  great  a  loss  of  volume  on  one  side  as  there  was  gain  on 
the  other,  so  that  the  situation  would  not  in  any  way  be  relieved. 
If,  on  the  other  hand,  we  take  the  reaction 

4HC1+O2  <=±  2C12+2H2O 

we  note  that  5  volumes  of  gas  on  the  left  unite  to  form  4  volumes  of  gas 
on  the  right.  Increase  in  total  pressure  here  will  be  attended  by  a 
shift 'ng  of  the  reaction  towards  the  right,  because  this  process  tends  to 
decrease  the  total  volume  and  thus  relieve  the  pressure.  This  means 
that  the  oxidation  of  hydrochloric  acid  gas  to  produce  chlorine  would  be 
more  effective  under  high  pressure. 

*  This  is  an  application  of  a  theorem  by  Le  Chatelier,  which  states  that  any 
equilibrium  tends  to  so  shift  itself  as  to  neutralize  the  effect  of  any  change  made 
upon  it. 


EFFECT  OF  CHANGES  IN  CONCENTRATION  203 

Effect  of  Changes  in  Concentration  on  Equilibrium. — We  may  best 
develop  the  general  law  here  by  again  making  use  of  our  stock  example, 
hydriodic  acid.  If,  when  hydriodic  acid  and  its  constituents  are  in 
equilibrium,  more  hydrogen  or  iodine  is  introduced,  so  as  to  increase  the 
concentration  of  this  constituent,  at  the  same  time  keeping  the  total 
pressure  of  the  system  constant,*  a  general  readjustment  will  imme- 
diately occur.  The  opportunities  for  favorable  impact  of  H^  and  12 
will  be  increased,  and  so  the  speed  of  the  forward  reaction,  H2+I2  <=^  2HI 
will  be  increased.  This  will  increase  the  concentration  of  the  HI,  and 
this  will  result  immediately  in  an  increase  in  the  speed  of  the  reverse 
reaction.  After  a  very  short  time  the  two  reactions  will  again  be  in 
equilibrium,  and  the  different  concentrations  will  then  be  found  to  have 
adjusted  themselves  so  that  the  relation  expressed  by  the  equilibrium 
constant  will  again  hold.  Note,  in  particular,  this  last  statement,  that 
the  ratio  expressed  by  the  constant  still  holds.  This  means  that  the 
value  of  the  constant  is  absolutely  independent  of  the  concentrations  of  the 
reacting  substances.  This  is  to  be  expected,  of  course;  for  in  developing 
the  general  formula  nothing  was  said  about  the  numerical  values  of 
the  concentrations;  and,  too,  in  working  out  the  value  of  K  for  the 
reaction  H2+l2^2HI,  widely  varying  concentrations  were  used, 
always  with  the  same  result. 

But  let  us  see  what  changes  in  concentration  must  have  occurred 
to  bring  about  the  equilibrium.  Suppose  the  concentration  of  the 
iodine  has  been  increased ;  what  must  now  be  the  concentrations  of  the 
other  substances?  If  (12)  is  increased,  its  interaction  with  H2  will  be 
favored,  and  the  latter  will  be  used  up  more  rapidly;  in  other  words, 
(H2)  will  be  lowered.  If  the  interaction  of  iodine  and  hydrogen  is 
favored  and  (HI)  thus  increased,  the  consequent  increase  in  the  reverse 
reaction  will  throw  back  the  hydrogen  and  iodine  more  rapidly.  The 
final  condition  when  equilibrium  is  again  established  will  be  as  follows: 
(I2)  will  be  higher,  (H2)  will  be  lower  in  somewhat  lesser  degree,  and 
(HI)  will  be  as  much  higher  as  (H2)  is  lower.  The  general  effect  of  the 
addition  of  iodine  has  been,  therefore,  to  favor  the  forward  reaction  and 
thus  increase  the  concentration  of  hydriodic  acid,  and  this  has  been 
accomplished  largely  at  the  expense  of  the  hydrogen. 

Addition  of  hydrogen  would  have  accomplished  about  the  same 
thing,  but  at  the  expense  of  the  iodine.  Addition  of  hydriodic  acid 
would  have  favored  the  reverse  reaction  and  so  would  have  increased 
the  concentrations  of  hydrogen  and  iodine. 

Note,  as  mentioned  above,  that  while  all  these  changes  in  concen- 
tration have  been  taking  place  the  adjustment  has  always  been  so 
*  Not  necessary  in  this  case,  but  generally  so. 


204  HOMOGENEOUS  EQUILIBRIUM 

perfect  that  the  ratio  expressed  by  the  equilibrium  constant,  K,  has 
not  changed  at  all,  provided  only  the  temperature  has  been  kept  con- 
stant. 

Note  also  that  the  equilibrium  has  not  necessarily  been  very  greatly 
displaced  by  the  increase  in  the  concentration  of  one  of  the  reacting  sub- 
stances because  this  process  also  increases  the  opposing  reaction.  We 
shall  now  describe  a  method  which  is  more  effective,  namely,  lowering 
the  concentration  of  one  of  the  reacting  substances.  If  in  the  above  inter- 
action of  hydrogen  and  iodine  we  wished  to  make  the  union  as  com- 
plete as  possible,  that  is,  if  we  wished  to  favor  the  forward  reaction,  we 
could  do  it  most  effectively  by  removing  the  product,  hydriodic  acid, 
as  fast  as  it  was  formed.  This  could  be  done  by  carrying  out  the  reac- 
tion in  the  presence  of  powdered  calcium  carbonate.  Neither  the 
hydrogen  nor  the  iodine  would  react  with  this,  but  the  acid  would  be 
completely  neutralized.  The  reverse  reaction  could  thus  be  entirely 
eliminated  and  the  forward  reaction  would  be  allowed  to  proceed  to 
completion. 

If  on  the  other  hand,  we  wished  to  cause  the  reverse  reaction  to  go 
to  completion,  we  could  do  so  by  arranging  to  remove  either  the  hydro- 
gen or  the  iodine  and  thus  eliminate  the  forward  reaction.  We  might 
arrange  to  carry  out  the  reaction  in  a  closed  tube  and  allow  one  end  of 
the  tube  to  remain  cold  while  the  rest  was  heated  to  440°.  The  iodine 
would  diffuse  into  the  cold  part  of  the  tube  and  condense  to  a  solid, 
thus  being  removed  quite  effectually  from  the  scene  of  action.  The 
final  condition  would  then  involve  the  almost  complete  breaking  up  of 
the  hydriodic  acid  into  hydrogen  gas  and  solid  iodine. 

It  should  be  noted  that  in  this  case,  as  in  the  former  case,  the  great 
changes  in  concentration  have  in  no  wise  affected  the  equilibrium  ratio. 
In  other  words,  the  value  of  the  constant  remains  the  same. 

Effect  of  a  Catalyst. — Many  substances  are,  under  certain  circum- 
stances, capable  of  greatly  increasing  or  decreasing  the  speed  of  certain 
reactions,  without  being  themselves  permanently  changed.  Such  sub- 
stances are  called  "  catalysts."  Thus,  manganese  dioxide  hastens  the 
evolution  of  oxygen  from  potassium  chlorate;  finely  divided  platinum 
(platinum  black)  hastens  the  rate  of  combination  of  certain  gases, 
notably  H2  and  62  to  form  water,  or  S02  and  62  to  form  SOs,  in  the 
contact  process  for  sulphuric  acid;  H+  ion  and  OH~  ion  hasten  the 
hydrolysis  of  an  ester  or  of  cane  sugar.  Water  often  acts  as  a  catalyst, 
for  many  reactions  are  immeasurably  slow  without  it.  Carbon  monox- 
ide will  not  burn,  for  example,  if  perfectly  dry.  The  decomposition  of 
hydrogen  peroxide,  on  the  other  hand,  is  retarded  by  the  presence  of  a 
small  amount  of  a  negative  catalyst,  called  "  acetanilide." 


THE  IONIZATION  OF  WEAK  ACIDS  AND  BASES  205 

Referring  to  the  effect  of  a  catalyst  on  reactions  in  equilibrium,  we 
note  that  in  all  such  cases  we  have  two  opposing  reactions;  and  it  hap- 
pens that  any  catalyst  which  will  hasten  one  of  the  reactions  will  also 
hasten  the  other  to  exactly  the  same  degree.  This  must  be  so,  for  if  it 
were  not  we  might  cause  a  reaction  to  go  in  one  direction  with  a  catalyst 
and  then,  by  simply  removing  the  catalyst  cause  this  reaction  to  go  in 
the  reverse  direction.  In  that  way  we  should  be  getting  work  done 
without  the  expenditure  of  any  energy,  which  we  know  is  impossible. 
Since  this  is  true,  the  application  of  a  catalyst  to  an  equilibrium  reaction 
can  never  shift  the  equilibrium  ratio  at  all.  What,  then,  can  a  catalyst  do? 
Just  this:  If  we  start  out  with  one  set  of  substances,  as  represented  by 
A  and  B,  and  wish  them  to  react  to  form  B  and  C  until  equilibrium  is 
established,  then  the  catalyst  can,  by  hastening  the  reactions,  greatly 
shorten  the  time  required.  Take,  for  example,  the  hydrolysis  of  ethyl 
acetate  as  represented  by  the  equation 

CH3COOC2H5+H2O  ±+  CH3COOH+C2H5OH 

If  we  mix  the  ester  and  water,  as  represented  on  the  left,  the  acid  and 
alcohol  are  slowly  formed,  and  these  immediately  begin  to  react  to 
regenerate  the  ester  and  water.  If  time  enough  is  allowed,  the  two 
opposing  reactions  finally  come  to  a  balance.  When  this  has  occurred 
the  ratio,  as  expressed  by  the  equation 

(CH3COOC2H5)  X  (H20) 
(CHsCOOH)  X  (C2H5OH)  ~ 

has  the  value  4.  But  these  reactions  are  extremely  slow;  without  the 
aid  of  a  catalyst  it  would  take  perhaps  a  month  at  ordinary  temperatures 
for  the  reaction  to  complete  itself.  In  the  presence  of  a  catalyst,  which 
in  this  case  may  be  an  acid  (H+ion),  the  reaction  is  very  much  accel- 
erated, and  the  establishment  of  equilibrium  is  accomplished  in  a  com- 
paratively short  time. 

We  may  now  repeat  what  we  said  before.  In  no  case  can  a  catalyst 
shift  an  equilibrium,  but  it  can  shorten  the  time  necessary  to  establish  a 
condition  of  equilibrium. 

The  lonization  of  Weak  Acids  and  Bases:  lonization  Constants. — 
The  ionization  of  any  weak  electrolyte  is  a  reversible  chemical  reaction 
subject  to  all  the  laws  of  equilibrium  discussed  above.*  We  can  best 

*  First  developed  by  Ostwald,  and  called  "  Ostwald's  Dilution  Law."  Zeitschr. 
physikal.  Chemie,  2,  278. 


206 


HOMOGENEOUS  EQUILIBRIUM 


discuss  this  matter  in  terms  of  concrete  examples.  Let  us  begin  with 
acetic  acid. 

Acetic  acid  when  in  solution  breaks  down  slightly  into  hydrogen  ions 
and  acetate  ions,  according  to  the  following  equation : 

HC2H302  ±+  H++C2H3O2- 

The  speeds  with  which  the  molecules  ionize  and  the  ions  recombine  are 
in  equilibrium  at  any  dilution.  We  should  therefore  expect  the  math- 
ematical form  of  the  equilibrium  equation  to  hold,  and  should  expect 
to  be  able  to  work  out  an  equilibrium  constant,  which  in  this  case  and  in 
all  cases  of  ionic  equilibrium  we  should  call  the  "  ionization  constant." 
We  shall  find  that  we  can  do  this  by  following  the  same  method  as  that 
employed  with  hydriodic  acid.  The  mathematical  form  of  the  equi- 
librium equation  will  be 


(H+)X(C2H302-) 
(HC2H3O2) 


=  K 


By  substituting  values  in  this  equation  we  can  find  the  value  for  K 
which,  as  in  any  case  of  equilibrium,  holds  for  any  concentration  but  for 
only  one  temperature.  To  obtain  the  necessary  concentration  values  we 
must  know  the  degree  of  ionization  of  the  acid  at  several  different  con- 
centrations. The  latter  may  be  calculated  from  conductivity  data  or 
by  any  of  the  methods  we  have  described.  We  give  below  the  neces- 
sary data  for  acetic  acid  at  several  different  dilutions.  The  problem  of 
working  out  the  values  is  left  to  the  student.  Column  1  gives  concen- 
trations, column  2  gives  conductivity  at  the  given  dilution  at  18°,  the 
other  columns  are  to  be  filled  in.  The  maximum  conductivity  for  acetic 
acid  is  347. 


Concentra- 

Conduc- 

Degree of 

tion  of  Acid 

tivities  . 

Ionization. 

(H+) 

(C2H302-). 

(HC2H302). 

K. 

0.1 

4.67 

0  i  'i  '-\' 

•  Ofb^ 

./ 

/.£x/0 

0.08 

5.22 

0.03 

8.50 

0.01 

14.50 

The  ionization  constant,  as  calculated  from  one  set  of  data,  is  1.8X 

io-5. 


THE   IONIZATION  OF  WEAK  ACIDS  AND   BASES 

The  ionization  constant  for  any  other  monobasic  acid  is  calcu 
in  exactly  the  same  way  as  that  for  acetic  acid. 

In  calculating  the  constants  for  polybasic  acids,  we  have  to  remember 
that  the  hydrogen  ion  concentration  is  to  be  raised  to  the  power  indi- 
cated by  the  basicity  of  the  acid.  Thus,  in  calculating  the  constant  for 
carbonic  acid  our  mathematical  equation  will  assume  the  form: 


(H+)2X(C03=) 
(H2C03) 


This,  of  course,  gives  the  constant  for  the  total  ionization.     If  we  want 
the  constant  for  the  primary  ionization  alone  we  should  have 

(H+)X(HCQ3-)_ 
(H2C03) 

or,  for  the  secondary,  we  should  have 

(H+)X(C03=) 
(HC03-) 


In  the  last  two  cases,  no  squaring  is  necessary  because  the  negative  ion 
only  reacts  once  with  the  hydrogen.  In  the  first  case,  the  reaction  very 
evidently  occurs  in  two  steps,  with  the  formation  of  HCO3~  as  an  inter- 
mediate compound. 

The  constants  for  weak  bases  are  worked  out  in  exactly  the  same 
way  as  for  acids  and  need  not  therefore  be  taken  up  in  detail.  It  must 
be  remembered,  of  course,  that  in  the  case  of  a  poly-acid  base,  like 
Mg(OH)2  or  La(OH)3,  the  OH  concentration  must  be  squared  or  cubed 
as  the  case  may  demand. 

The  following  tables  give  the  ionization  constants  for  several  of  the 
commoner  weak  acids  and  bases.*  Under  the  head  of  "  equilibrium 
ratio  "  in  each  case,  is  indicated  just  what  kind  of  ionization  the  con- 
stant refers  to,  whether  primary,  secondary,  or  tertiary,  for  example, 
and  just  what  is  included  in  the  ratio  in  any  given  case. 

*  For  a  list  of  references  on  ionization  constants,  see  Stieglitz,  Qualitative 
Analysis,  Vol.  I,  pp.  104,  106,  107  (1911). 


208 


HOMOGENEOUS  EQUILIBRIUM 


IONIZATION  CONSTANTS 
Table  1.     Acids. 


Acid. 

Equilibrium  Ratio. 

K. 

Oxalic  (p) 

(H+)X  (HC2O4-)/(II2C2O4) 

3.8X10"2 

Oxalic  (s)  

(H+)X  (C2O4=)/(HC,O4-) 

5X10"5 

Phosphoric  (p)  
Phosphoric  (s) 

(H+)X(H2P04-)/(H3P04) 
(H+)X  (HPO4=)/(H2PO4-) 

ID"2 
2xlO~7 

Phosphoric  (0  

(H  +  )  X  (PO4=)  /  (HPO4=  ) 

4X10~13 

Arsenic  (p)  

(H+  )  X  H2AsO4-/H3AsO4 

5X10~3 

Nitrous 

(H+)X  (NO2~)/(HNO2) 

5X10~4 

Acetic 

(H+)X  (C2H3O2~)/HC2H3O2 

1.8X10"5 

Carbonic  (p). 

(H+)X  (HCO3-)/H2CO3)  +  (CO2) 

3X10~7 

Carbonic  (s) 

(H+)X(CO8~)/(HCOj~) 

7X10"11 

Hydrosulphuric  (p)  
Hydrosulphuric  (s)      .  . 

(H+)X(HS-)/(H2S) 
(H+)X(S=)/(HS~) 

9X10~8 
10~15 

Boric  (p) 

(H+)X  (H2BO3~)/(H^BO3) 

7X10~10 

Hydrocyanic  

(H+)X(CN~)/(HCN) 

7X10~10 

Table  2.     Bases. 


Base. 


Equilibrium  Ratio. 


K. 


Ammonium  hydrox- 
ide  

Aniline 

Hydrazene 


(NH4+)X(OH-)/(NH4 
(C6HSNH2+)X(OH-) 


/C6H5NH3OH)  +  (C6H6NH2)  l 
(N2H5+)X  (OH~)  /(N^HsOH)  +N2H4)] 


1.8X1Q-5 

5X10-10 
3X10~6 


1  In  ordinary  calculations  we  count  everything  under  the  vinculum  as  hydroxide, 
e.g.,  NH4OH+NH3  is  counted  as  NH4OH.  For  the  actual  relation  between  NH3 
and  NH4OH  and  the  strength  of  NH4OH  as  a  base,  see  T.  S.  Moore,  Jour.  Chem. 
Soc.,  91,  1379, 

Ion  Concentrations  from  lonization  Constants. — Perhaps  no  set  of 
chemical  constants  is  of  more  value  than  are  the  ionization  constants  of 
acids  and  bases  when  their  use  is  really  understood.  One  use  of  great 
value  is,  of  course,  found  in  the  working  out  of  equilibrium  relations. 
This  will  appear  as  we  "proceed.  Another  important  use  is  in  the  deter- 
mination of  ionic  concentrations  and  degrees  of  ionization.  This  we 
may  describe  here: 


ION  CONCENTRATIONS  FROM  IONIZATION  CONSTANTS     209 

The  method  we  have  used  so  far  in  determining  degree  of  ionization 
has  involved  the  use  of  conductivity  or  freezing-point  data,  and  these  are 
usually  given  only  for  a  few  definite  concentrations.  Thus,  in  the  case  of 
acetic  acid  (page  206)  we  had  the  data  only  for  the  concentrations  0.1, 
0.08,  0.03,  and  0.01.  We  were  able  then  to  work  out  the  degrees  of 
ionization  and  the  ionic  concentration  for  these  concentrations  only. 
N|ow  our  point  is,  that  by  use  of  our  ionization  constants  we  can  work 
out  these  values  for  any  concentration.  It  is  understood,  of  course,  that 
the  constant  itself  has  been  worked  out  originally  from  conductivity 
data  or  other  data  of  that  sort;  but  when  once  known  it  enables  us  to 
fill  in  the  values  for  concentrations  not  previously  known,  just  as  a 
solubility  curve  does  for  solubility  values. 

Suppose,  for  example,  we  want  to  know  the  concentration  of  H+ 
ion  or  acetate  ion  in  0.05  molar  acetic  acid.  The  equilibrium  ratio  for 
acetic  acid  is  represented  thus: 

(H+)X(C2H302-) 
(HC2H302) 

The  concentrations  for  hydrogen  ion  and  acetate  ion  in  a  solution  of 
pure  acetic  acid  will  necessarily  be  equal,  because  every  molecule  of 
acid  which  ionizes  gives  one  of  each  of  these  ions.  We  may  therefore 
represent  their  concentration  by  x,  and  the  product  of  the  two  will  then 
be  x2.  The  non-ionized  part,  represented  by  (HX^HaCfe),  will  be  the 
total  concentration  minus  the  ionized  part.  In  this  case  this  will  be 
0.05 — x,  We  may  therefore  write 

=  1.8X10~5 


0.05  -x 

From  this,  £2=0.09X10-5-1.8XlO-5z.  This  is  a  quadratic  equation 
and  will,  of  course,  give  two  values  for  x.  These  values  are  +  0.922X 
10~3  and  —  0.958  X10~3.  Obviously,  only  the  positive  value  is  pos- 
sible, and  this  is  better  written  9.22X10"4.  This  value  for  x  is,  then, 
the  concentration  of  the  H+  ion  or  the  acetate  ion  in  0.05  molar  acetic 
acid. 

But,  since  x  is  a  very  small  number,  it  is  evident  that  the  value 
0.05  —  x  might  almost  as  well  be  left  simply  as  0.05  for  purposes  of  cal- 
culation, We  should  then  have 


210  HOMOGENEOUS  EQUILIBRIUM 


From  this,  Z2=0.09X10-5  and  x  =  v  0.09X10-  5,  or  9.4XKM.*  This 
value  for  x  is  then  the  concentration  of  either  the  H+  ion  or  the  acetate 
ion  in  0.05  molar  acetic  acid.  Note  that  this  value  differs  only  very 
slightly  from  the  more  accurate  value  determined  above. 

This  second  and  simpler  method  may  be  used  in  practically  any  case 
where  an  ionization  constant  exists,  for  in  all  such  cases  the  ion  concen- 
tration will  be  small. 

Having  the  concentration  of  the  ions  and  the  total  concentration,  we 
may  also  calculate  the  degree  of  ionization,  if  we  like.  Thus  the  ion 
concentration  is  ordinarily  obtained  by  multiplying  the  total  concen- 
tration by  the  degree  of  ionization.  The  degree  may  therefore  be  cal- 
culated by  dividing  the  ion  concentration  by  the  total  concentration. 
The  degree  in  the  case  of  0.05  molar  acetic  acid  will  then  be 

9.4X10-4 

^ 


This  may  be  written  as  0.019  or  1.9  per  cent. 

If  we  apply  our  ionization  constants  to  the  working  out  of  the  con- 
centrations of  the  secondary  and  tertiary  ions  in  the  presence  of  the  pri- 
mary, we  make  the  rather  surprising  discovery  that  their  numerical 
values  equal  the  constants,  regardless  of  the  total  concentrations.! 
Take  the  case  of  carbonic  acid  : 

The  constant  for  the  primary  ionization  (H^COs  *=>  H+H-HCOs") 
is  3X10~7.  The  concentrations  of  the  ions  are  equal:  call  them  x. 
The  concentrations  of  the  non-ionized  part  (EfeCOs)  in,  say,  M/100 
solution  is  practically  0.01.  We  therefore  have  x2/0.01  =  3X10~7;  and, 
solving  for  x,  we  obtain  for  either  (H+)  or  (HCOs")  the  value  5.4  X  10~5. 

The  constant  for  the  secondary  ionization  (HCOs"  *=»  H+COs=) 
is  7X10~n.  Since  the  secondary  ionization  is  so  small,  the  factors 
(H+)  and  HCOs~)  here  may  be  taken  as  identical  with  those  just  cal- 
culated above.  Substituting  values,  therefore,  we  have 

5.4X10-5X(CO3=) 


5.4X10 


-5 


=  7XlO-n 


From  this  we  see  that  the  concentration  of  the  C03=  is  7XlO~n 
(equal  to  the  constant,  as  stated  above). 

*  To  determine  the  square  root  of  a  number  having  an  odd  exponent,  convert  it 
into  a  number  having  an  even  exponent.  Thus  0.09X10"5  may  be  written  0.9X 
10~6.  •  The  square  root  of  this  is  0.94X  10~3,  better  written  as  9.4X10"4. 

t  The  secondary  ionization  of  sulphuric  acid,  HSO4~— >  H+  +SO41",  gives  a  fairly 
good  constant  whose  value  is  about  0.03.  With  a  constant  of  this  size,  this  rule 
would  not  hold. 


IONIZATION   AND   STRONG  ELECTROLYTES  211 

To  be  perfectly  exact,  of  course,  the  value  for  (H+)  in  the  above 
equation  should  be  increased  by  about  7X10~n  (the  secondary  H+)  and 
the  value  for  (HCOs")  should  be  decreased  by  the  same  amount;  but  it 
is  perfectly  obvious  that  this  change  would  make  no  appreciable  differ- 
ence with  the  value  for  (COs"")  resulting  from  the  secondary  ionization. 

If  the  total  concentration  of  the  carbonic  acid  were  increased  the 
values  for  the  primary  ions  would  be  increased;  but,  since  these  values 
practically  cancel  out,  the  secondary  would  remain  the  same.  In  other 
words  the  values  for  the  secondary  ions  are  independent  of  the  total 
concentration,  as  stated. 

If  we  count  on  the  primary  hydrogen  being  first  neutralized,  then  the 
case  is  very  different.  We  shall  than  have  an  acid  salt,  such  as  NaHCOs 
or  NaH2P04,  which,  as  is  general  with  salts,  will  be  highly  ionized, 
giving  a  high  concentration  of  the  primary  negative  ion  (e.g.,  HCOa"). 
This  ion  will  give  its  secondary  ionization  more  freely  than  in  the  pres- 
ence of  the  primary  hydrogen  because  of  the  absence  of  the  common  ion 
effect,  and  will  give  equal  amounts  of  its  two  ions.  It  may,  therefore, 
be  regarded  as  a  pure  acid,  and  the  concentrations  of  its  ions  may  be 
calculated  by  use  of  its  constant  exactly  as  in  the  case  of  acetic 
acid. 

Ionization  of  Strong  Electrolytes. — The  law  of  ionic  equilibrium 
applies  to  all  weak  electrolytes.  This  class  includes  practically  all  the 
organic  acids,  hundreds  in  number,  most  of  the  organic  bases,  ammonium 
hydroxide  and  a  few  other  weak  inorganic  bases,  and  all  weak  inorganic 
acids,  like  boric,  hydrosulphuric,  etc.  It  does  not  apply  to  the  strong 
electrolytes.*  In  this  class  we  have  the  strong  acids,  like  hydrochloric, 
nitric,  and  sulphuric,  the  strong  bases,  like  sodium  hydroxide  and 
potassium  hydroxide,  and  all  the  salts  with  one  or  two  exceptions, 
namely  certain  salts  of  mercury. 

What  we  mean  by  saying  that  the  law  does  not  apply  in  the  latter 
case  is  this:  If  we  determine  the  concentrations  of  the  ions  and  of  the 
nonrionized  molecules  for  different  dilutions  and  substitute  these  values 
in  our  equation,  we  do  not  obtain  a  constant.  As  the  total  concen- 
trations of  the  electrolytes  are  increased,  the  values  of  what  should  be  a 
constant  in  each  case  also  increase.  This  means  that  these  electrolytes 
are  too  strongly  ionized  in  the  more  concentrated  solutions.  Take 
potassium  chloride  as  an  example.  Where  the  total  concentration  is 
0.001,  the  "  constant,"  as  determined  from  conductivity  data,  is  0.035; 
for  a  concentration  of  0.01  it  is  0.130;  and  for  a  concentration  of  0.1  it  is 
0.485. 

*  A  slight  discrepancy  is  found  in  the  case  of  some  weak  electrolytes.  See,  in 
this  connection,  Wegscheider,  Zeitschr.  physikal.  Chemie,  69,  603  (1909). 


212  HOMOGENEOUS  EQUILIBRIUM 

The  reason  for  this  discrepancy  we  must  frankly  acknowledge 
we  do  not  yet  know.  It  has  been  suggested  that  the  "  salt  effect  " 
may  be  partially  responsible  for  it,  or  it  may  be  due  to  the  effect  of  an 
accumulation  of  charged  particles  (ions).  We  have  shown  that  neutral 
salts,  like  sodium  chloride,  do  seem  to  increase  ionization,  so  it  is  not  at 
all  impossible  that,  in  concentrated  solutions,  the  molecules  of  elec- 
trolytes may  aid  the  water  in  effecting  their  own  ionization.  Note  in 
this  connection  that  molten  salts  are  ionized.  As  to  the  effect  of 
charged  particles,  equilibrium  is  supposed  to  be  a  matter  of  molecular 
motion  and  impact  between  particles  which  do  not  attract  or  repel  each 
other.  In  cases,  however,  where  the  number  of  charged  particles 
becomes  large,  as  in  concentrated  solutions  of  strong  electrolytes,  it  is 
hardly  to  be  expected  that  the  electrical  attractions  and  repulsions 
should  be  negligible  factors. 

Whether  we  can  explain  the  discrepancy  or  not,  we  are  not  to 
discard  the  law  of  ionic  equilibrium  simply  because  we  find  some  cases 
to  which  it  alone  does  not  apply.  We  do  not  discard  Van't  Hoff's  appli- 
cation of  the  gas  laws  to  solutions  because  solutions  of  electrolytes 
offer  some  seeming  exceptions.  We  shall  sometime  know  why  the  dis- 
crepancies exist,  just  as  we  now  know  the  reason  for  van't  Hoff's  excep- 
tions. 

Displacement  of  Ionic  Equilibrium. — For  the  displacement  of  ionic 
equilibrium,  we  have  at  our  disposal  the  two  methods  described  under 
the  general  discussion  above,  namely,  change  of  temperature  and 
change  of  concentration.  The  first  method  we  shall  not  discuss. 
Under  the  head  of  the  second  method  it  will  be  remembered  that 
we  discussed  two  possible  methods  of  procedure.  One  was  an 
increase  in  the  concentration  of  one  of  the  reacting  substances, 
tending  thus  to  force  the  reaction  forward:  the  other  involved  a 
decrease  in  the  concentration  of  one  of  the  products  of  a  reaction, 
tending  to  prevent  reversal.  These  same  methods  are  used  in 
ionic  equilibrium.  The  first  usually  goes  under  the  name  "  common 
ion  effect"  The  second  is  not  usually  named,  but  we  shall  call  it  the 
"  neutralization  effect" 

The  Common  Ion  Effect. — The  common  ion  effect  is  brought  abou 
by  adding  to  the  solution  of  a  weak  electrolyte  some  strong  electrolyte 
having  one  ion  in  common  with  it.  Thus,  to  a  weak  acid  we  add  either 
a. strong  acid  giving  H+  ion  in  common,  or  a  salt  of  the  original  acid, 
giving  the  negative  ion.  To  a  weak  base  we  add  a  strong  base,  giving 
OH~  ion,  or  a  salt  of  the  original  base,  giving  the  positive  ion.  Just 
what  the  effect  is  can  best  be  shown  by  examples.  Take  first  acetic 
acid: 


THE  COMMON  ION  EFFECT  213 

We  have  seen  that  acetic  acid  ionizes  according  to  the  equation 

HC2H3O2  <=±  H+-f  C2H3O2- 

and  that  the  ions  and  the  undissociated  molecules  are  in  equilibrium, 
as  represented  by  the  equation 

(H+)X(C2H302-) 
(HC2H302) 

We  may  increase  the  concentration  of  the  acetate  ion  by  adding  sodium 
acetate.  This  salt,  like  most  other  salts,  is  highly  ionized  and  thus 
gives  a  high  concentration  of  acetate  ion.  If  we  thus  increase  the  con- 
centration of  the  acetate  ion  we  shall  favor  the  recombination  of  this  ion 
with  hydrogen  ion,  and  more  non-ionized  acetic  acid  will  be  formed. 
This  will,  of  course,  lower  the  concentration  of  the  hydrogen  ion,  as  can 
be  seen  by  noting  the  quantitative  relations.  Suppose,  for  example, 
we  start  with  molar  acetic  acid,  and  then  add  to  the  solution  an  equiva- 
lent amount  of  solid  sodium  acetate.  Molar  acetic  acid  is  0.0042 
(  =0.42  per  cent)  ionized.  The  concentration  of  the  ions  will,  therefore, 
be  0.0042  each,  and  that  of  the  non-ionized  molecules  will  be  0.9958. 
Substituting  in  our  equation  we  have 

0.0042X0.0042 
0.9958 

Molar  sodium  acetate  is  0.53  (53  per  cent)  ionized,  so  that  the  addition 
of  an  equivalent  amount  of  this  salt  (1  mole  per  liter)  will  increase  the 
acetate  ion  concentration  by  0.53,  making  the  total  concentration  of  this 
ion  0.5342.  We  should  then  have  the  relation 

0.0042X0.5342 
0.9958        > 

But  change  of  concentration  should  not  change  the  value  of  the  con- 
stant. Therefore  the  concentrations  will  immediately  adjust  them- 
selves so  that,  the  original  ratio  again  holds.  As  stated  above,  this  can 
be  accomplished  only  by  combination  of  the  ions  to  form  non-ionized 
acid.  If  we  let  x  equal  the  fraction  of  a  mole  thus  combined,  it  is 
evident  that  the  concentration  of  each  ion  will  be  decreased  by  x  moles 


214  HOMOGENEOUS   EQUILIBRIUM 

and  the  concentration  of  the  non-ionized  part  will  be  increased  by  the 
same  amount.  We  shall  then  have 

(0.0042  -x)X  (0.5342  -x)  _ 
(0.9958+z) 

From  this  x  is  found  to  be  0.004166  mole.  If  we  subtract  this  value 
from  the  ion  concentrations  and  add  it  to  the  non-ionized  part  we  have, 
as  a  final  result  after  the  adjustment, 

0.000034X0.53=18><10_5 

If  we  examine  the  values  carefully,  we  find  that,  in  spite  of  the  great 
change  in  the  individual  concentrations  of  the  ions,  the  product  of  the 
two  concentrations  remains  almost  what  it  was  before  the  common  ion 
effect  occurred.  One  is  very  much  larger,  but  the  other  is  smaller  in 
the  same  proportion.  This,  of  course,  is  due  to  the  fact  that  the  acid  is 
very  slightly  ionized,  making  it  impossible  greatly  to  change  the  value  of 
the  non-ionized  part.  What  is  true  here,  then,  would  be -true  for  any  other 
concentration  of  acetic  acid,  provided  the  ionization  is  slight. 

When  we  know  this  fact  of  the  constancy  of  the  ion  product  for  any 
given  concentration,  the  calculation  of  the  common  ion  effect  is  very 
much  simplified.  Thus,  for  molar  acetic  acid,  we  have  very  nearly 

(H+)X(C2H302-)=1.8X10-5 

If,  therefore,  the  acetate  ion  concentration  is  made  0.5342,  we 
have  (H+)X0.5342  =  1.8X10-5  and  (H+)  =1.8X10~5/0.5342,  or 
0.000034.  For  0.05  molar  acetic  acid,  we  should  have  very  nearly 
(H+)  X  (C2H302-)/0.05  =  1.8  X 10-5  and  (H+)  X  (C2H3O2-)  =  (nearly) 
0.05  X  1.8  X10~5,  or  0.09  X10~5.  If  in  this  case  also  we  fix  a  value  for 
one  of  the  ion  concentrations  the  other  can  be  calculated  exactly  as 
with  the  molar  acid. 

The  common  ion  effect  with  a  weak  base  follows  exactly  the  same 
course  as  with  a  weak  acid,  and  so  need  not  be  described  here. 

The  Neutralization  Effect. — We  have  said  that,  in  using  the  neutrali- 
zation effect  we  prevent  reversal  by  lowering  the  concentration  of  one  or 
more  of  the  products  of  a  reaction.  Since  there  is  no  limit  to  the 
extent  to  which  the  concentration  of  a  product  can  be  lowered,  it  is 
evident  that  by  correct  procedure  a  reaction  could  in  this  way  be  made 


THE   NEUTRALIZATION  EFFECT  215 

to  go  to  completion  in  one  direction.  It  is,  therefore  a  very  effective 
method  of  disturbing  ionic  equilibrium. 

As  in  the  case  above,  we  can  best  discuss  this  matter  by  use  of  exam- 
ples. Take  first  the  mutual  neutralization  of  acids  and  bases,  as,  for 
example,  sodium  hydroxide  and  hydrochloric  acid: 

Sodium  hydroxide  furnishes  Na+  and  OH~  ions,  and  hydrochloric 
acid  furnishes  H+  and  Cl~  ions.  In  each  case  an  equilibrium  is  estab- 
lished as  shown  by  the  following  equations; 

(1)  NaOH<=±Na++OH- 

(2)  HC1<=±H+    +C1- 

Therefore,  neither  of  these  reactions  goes  to  completion  except  at  great 
dilution.  If,  however,  by  mixing  sodium  hydroxide  and  hydrochloric 
acid  we  allow  the  two  reactions  to  occur  in  the  same  solution,  two  other 
equilibria  are  immediately  brought  into  play.  The  first  is  that  between 
H+  and  OH~  and  the  product  of  their  combination,  H^O;  the  second  is 
that  between  Na+  and  Cl~,  and  their  product  NaCl.  This  can  be  best 
seen  from  the  following; 

(3)  NaOH<=»Na+=OH- 

HC1     <=»  Cl-  +H+ 

it        it 
NaCl    H2O 

The  tendency  towards  the  formation  of  NaCl  is  very  slight  unless 
the  solutions  are  very  concentrated,  because  this  compound  tends  to 
remain  in  the  ionic  condition.  (Note  the  heavy  arrow.)  A  slight 
amount  will,  however,  be  formed,  and  the  concentrations  of  Na  and  Cl 
will  thus  be  slightly  lowered.  This  very  slightly  disturbs  the  upper 
equilibria  towards  the  right;  in  other  words,  slightly  increases  the 
ionization  of  the  NaOH  and  the  HC1.  But  with  the  other  equilibrium 
the  case  is  vastly  different.  Water,  the  product  of  the  reaction,  we 
know  to  be  scarcely  at  all  ionized.  Non-ionized  water  is  therefore  bound 
to  be  formed  until  either  the  H+  or  the  OH~  or  both  are  exhausted. 
(Note  the  heavy  arrow  here  also.)  This  means  the  almost  complete 
elimination  of  any  reunion  of  the  ions  Na+  and  OH~  or  of  Cl~  and  H+; 
in  other  words  it  prevents  a  reversal  of  the  original  reactions,  (1)  and 
(2),  and  allows  them  to  go  to  completion  towards  the  right. 


216  HOMOGENEOUS  EQUILIBRIUM 

As  a  second  example  we  shall  take  the  neutralizing  effect  seen  when 
the  salt  of  a  weak  add  is  added  to  a  solution  of  a  stronger  acid.  Thus, 
when  we  mix  sodium  acetate  with  hydrochloric  acid,  we  have  repre- 
sented the  following  equilibria  : 


NaC2H302  ±+  C2H302-+Na+ 

4T      tl 

HC2H302    NaCl 

If  both  the  acid  and  the  salt  are  of  molar  concentration  (after  mixing) 
we  shall  at  first  have  present  a  concentration  of  H+  and  Cl~  of  about 
0.8,  and  of  C2H3O2-,  and  Na+  of  about  0.53.  But,  from  the  discussion 
of  page  213  we  remember  that  in  molar  solution  the  concentrations  of 
acetate  ion  and  hydrogen  ion  can  only  be  0.0042  if  they  are  to  remain  in 
equilibrium.  These  two  ions  will,  therefore,  instantly  combine  to  form 
acetic  acid,  until  the  concentrations  of  both  are  reduced  to  the  equi- 
librium value.  With  this  procedure  we  have,  therefore,  neutralized  the 
hydrochloric  acid  until  the  concentration  of  the  hydrogen  ion  is  barely 
0.0042. 

By  adding  an  excess  of  sodium  acetate  we  can  bring  into  play  the 
common  ion  effect  described  above  and  can  t.hus  still  more  effectually 
neutralize  the,  acid.  Thus,  if  we  add  to  the  mixture  already  formed 
another  equivalent  of  the  salt,  we  shall  have  duplicated  exactly  the  con- 
ditions described  on  pages  213  and  214,  and  shall  have  reduced  the 
hydrogen  ion  concentration  to  0.000034  (3.4X10~5),  which  is  beyond 
the  end  point  of  methyl  orange. 

Sodium  carbonate  is  a  salt  of  a  still  weaker  acid  than  acetic,  and  is 
therefore  still  more  effective  than  sodium  acetate  for  neutralizing  pur- 
poses. As  seen  when  we  were  discussing  the  titration  of  polybasic 
acids,  there  are  two  possibilities:  one  involving  the  formation  of  the 
bicarbonate  ion,  the  other  the  formation  of  carbonic  acid.  The  follow- 
ing equilibria  show  this  : 

(1)  Na2CO3  ±^  2Na++C03" 


u 

HC03- 
(2)  HC1<=±C1-    +H+ 

Ti 

H2CO3 


COMMON   ION   EFFECT  IN   TITRATION  217 

If  one  equivalent  of  acid  is  mixed  with  1  mole  of  carbonate  the  hydrogen 
ion  concentration  is  reduced  to  the  turning  point  of  phenolphthalein. 
In  other  words,  the  solution  is  not  merely  made  neutral  but  is  actually 
made  slightly  alkaline.  If  two  equivalents  of  acid  are  mixed  with  1  mole 
of  carbonate  the  solution  is  not  made  quite  neutral,  but  the  acidity  is 
brought  down  to  the  turning  point  of  methyl  orange  (2X10~4)  . 

Note  that  in  this  case,  as  with  sodium  acetate,  the  action  involves 
merely  a  removal  of  the  products  of  the  original  reactions,  thus  pre- 
venting reversal  and  allowing  these  reactions  to  proceed  to  completion. 
Sodium  carbonate  and  hydrochloric  acid  never  could  have  gone  com- 
pletely over  into  the  ionic  condition  if  we  had  not  thus  removed  one  of 
the  ions  in  either  case.  The  fact  that  after  the  reactions  nothing  remains 
in  the  solution  but  Na+,  Cl",  and  H2CO3,  is  merely  incidental. 

It  should  be  mentioned  that  one  reason  why  the  second  reaction 
above  proceeds  so  nearly  to  completion  is  the  fact  that  a  large  portion 
of  the  carbonic  acid  produced  breaks  up  and  escapes  as  gaseous  CO2, 
thus  lowering  its  concentration.  We  mention  this  because  the  matter 
of  volatility  is  an  important  factor  in  many  neutralization  reactions. 

Another  factor  closely  related  to  volatility  is  the  matter  of  insolu- 
bility. If  an  insoluble  compound  is  formed  by  union  of  certain  ions 
these  ions  will,  of  course,  be  almost  completely  removed  from  the  scene 
of  action,  and  the  parent  reactions  producing  these  ions  may  then  pro- 
ceed to  completion.  Thus  we  have  the  ionization  reactions  of  hydro- 
chloric acid  and  silver  nitrate,  neither  of  them  ordinarily  going  to  com- 
pletion. When  solutions  containing  these  two  substances  in  equivalent 
amounts  are  mixed,  however,  insoluble  silver  chloride  is  produced  by 
union  of  two  of  the  ions,  and  the  parent  reactions  then  proceed  to  com- 
pletion. The  following  equilibria  indicate  the  course  of  the  reactions: 


HC1<=»C1-+H+ 

4T 

AgCl  (nearly  insoluble) 

Common  Ion  Effect  in  Titration.  —  In  our  study  of  indicators  we 
noted  that  in  the  titration  of  a  weak  acid  or  base  the  end  point  with 
certain  indicators  appeared  before  the  reaction  was  completed.  Take, 
for  example,  the  titration  of  acetic  acid  with  sodium  hydroxide  with 
methyl  orange  indicator:  the  hydrogen  ion  was  reduced  below  the  turn- 
ing point  of  the  indicator  before  an  equivalent  amount  of  base  had  been 
added.  In  the  light  of  our  discussion  above  this  is  easily  explained. 
As  sodium  hydroxide  is  added  to  acetic  acid,  sodium  acetate  is  pro- 


218  HOMOGENEOUS  EQUILIBRIUM 

duced,  and  this,  as  we  have  seen  above,  suppresses  the  ionization  of  the 
remaining  acetic  acid.  Thus,  by  the  time  perhaps  half  the  acid  has 
been  neutralized  the  hydrogen  ion  may  already  have  been  reduced 
below  the  turning  point  of  the  indicator.  Perhaps  a  better  way  to  say 
this  would  be  that  as  the  hydrogen  ion  is  removed  to  form  water  with 
hydroxyl,  the  acetate  ion  is  allowed  to  accumulate  ;  and,  since  the  hydro- 
gen ion  must  always  be  in  equilibrium  with  this  acetate  ion,  its  concen- 
tration must  grow  smaller  as  that  of  the  acetate  ion  grows  larger.  The 
following  equilibria  make  this  clearer: 

decreasing  increasing 

HC2H3O2  <=±  H+     +  C2H3O2- 
NaOH  ±+  OH-  +Na+ 

4T 

H2O 

Phenolphthalein  works  satisfactorily  in  this  case  because  its  turning 
point  comes  where  the  H+  ion  concentration  is  very  small. 

The  titration  of  ammonium  hydroxide  with  hydrochloric  acid  involves 
the  removal  of  hydroxyl  and  the  accumulation  of  ammonium  ion.  The 
hydroxyl  concentration  is  thus  suppressed  and  the  solution  becomes 
acid  too  soon  for  phenolphthalein,  while  methyl  orange  gives  a  satis- 
factory result.  The  equilibria  involved  are  as  follows  : 

increasing        decreasing 
+OH- 


HC1  <=±  Cl-       +H+ 

it 
H2O 

Equilibrium  Relations  of  Water.  —  The  purest  water  ever  prepared 
shows  a  slight  conductivity,  thereby  indicating  a  slight  ionization. 
As  determined  by  five  or  six  different  methods,*  including  the  con- 
ductivity method,  the  fraction  of  a  mole  (18  gm.)  ionized  in  1  liter  at 
20°  C.  is  10~7,  or  0.000,000,1  mole  per  liter.  The  ionization  constant 
for  water  should  be  obtained  by  substituting  values  in  the  equation, 

(H+)X(OH-)_ 

(H20) 

*For  summary  of  methods  and  references,  see  Hudson,  Jour.  Am.  Chem.  Soc.,  31, 
1176  (1909).  See  also  remarks  by  van't  Hoff,  Lectures  on  Phys.  Chem.,  Vol.  I, 
p.  131. 


EQUILIBRIUM   RELATIONS  OF  WATER 


219 


The  concentration  of  H20  (non-ionized)  in  pure  water  is  1000/18 
or  55  molar  This  may  be  stated  as  0.55  X102.  Substituting  values, 
we  obtain  for  K: 

io-7xio-7 


But  the  concentration  of  the  non-ionized  water  is  practically  a  con- 
stant, even  in  solutions  of  moderate  concentration.  We  may,  therefore, 
say  thai  the  product  (H+)X(OH~)  is  also  a  constant.  The  value  of 
this  product  at  20°  is  10~14.  This  is  usually  termed  the  ionization  con- 
stant for  water,  often  indicated  by  Kw. 

The  constancy  of  this  ion  product  for  water  carries  with  it  some 
important  consequences.  It  means,  for  example,  that  even  in  solutions 
of  acids  where  (H+)  is  large,  or  in  solutions  of  bases  where  (OH~)  is 
large,  the  product  (H+)X(OH~)  will  have  the  constant  value  of  10~14. 
This  explains  at  once  why  in  the  table  of  indicators  (q.v.)  the  exponents 
of  10  for  (H+)  and  (OH~)  always  give  the  sum  —  14.  From  this  we  are 
also  able  to  calculate  the  concentration  of  the  one  ion  from  that  of  the 
other.  Thus  in  a  normal  solution  of  HC1  the  concentration  (H+)  is 
about  0.8;  and  since 

0.8X(OH-)  =  10-14 
(OH-)  must  be 

1.25  X10-14 

instead  of  10~7,  as  in  pure  water. 

The  temperature  effect  on  the  ionization  of  water  is  large.  This  is 
probably  due  to  the  fact  that  water  is  made  up  largely  of  complex 
molecules  which  at  higher  temperatures  dissociate  into  the  simple 
molecules,  the  latter  being  the  ones  which  are  really  in  equilibrium  with 
the  ions.  The  following  table  shows  how  rapidly  the  ion  product 
increases  with  rising  temperature  :  * 


0° 

18° 

25° 

75° 

100° 

306° 

0.05X10-14 

0.8X10~14 

1.2X10-14 

16.9X10~14 

48X10-11 

166X10-'4 

Note  that  at  about  20°  C.  (room  temperature)  the  ion  product  for 
water  is  1 X  10~14.  This  is  the  value  we  have  used  in  our  calculations 
because  we  have  assumed  that  the  operations  involved  were  performed 
at  room  temperature.  It  is  quite  evident  that  this  assumption  was 
necessary. 

*  Washburn,  Physical  Chemistry,  p.  365  (1921). 


220  HOMOGENEOUS  EQUILIBRIUM 

Hydrolysis  of  Salts.  —  Hydrolysis,  as  the  name  indicates,  is  a  breaking 
up,  or  decomposition,  of  salts  caused  by  water,  in  reality  by  the  ions 
of  water,  H+  and  OH~.  We  shall  discuss  four  cases: 

(a)  Hydrolysis  of  the  salt  of  a  strong  base  and  a  strong  acid,  e.g., 
NaCl  or  NaNOs;  sodium  chloride  is  the  salt  of  the  strong  base,  NaOH 
and  the  strong  acid,  HC1.  In  solution  it  ionizes  strongly  into  Na+  and 
Cl~.  Water,  as  we  have  seen  above,  ionizes  very  slightly  into  H+ 
and  OH~.  When  these  two  substances  are  in  contact,  as  in  a  water 
solution  of  sodium  chloride,  we  have  the  following  equilibria  represented  : 

Na+    +01- 


H20  <=±  OH- 

tl       tl 
NaOH     HC1 

The  concentrations  of  Na+  and  Cl~  will  ordinarily  be  large  (0.68  in 
molar  solution);  those  of  H+  and  OH~  will  be  very  small  (10~7). 
Now,  since  NaOH  and  HC1  are  both  very  highly  ionized,  we  should 
expect  here  practically  no  tendency  towards  the  formation  of  the  non- 
ionized  acid  or  base.  In  other  words,  sodium  chloride  under  ordinary 
conditions  should  not  be  appreciably  hydrolyzed.  In  practice  we  find 
that  it  is  not. 

At  high  temperatures  the  case  is  somewhat  different.  As  noted 
above,  the  ions  of  water  are  in  equilibrium  with  monohydrol.  At  high 
temperatures  the  proportion  of  this  is  very  much  increased,  and  there- 
fore the  concentrations  of  the  ions  are  much  larger.  We  might  expect 
from  this  a  much  more  marked  hydrolytic  action;  and  this  we  do  find  in 
practice,  as  the  following  example  *  will  show.  A  small  amount  of 
sodium  chloride  is  melted  in  a  platinum  crucible  and  maintained  at  a 
bright-red  heat.  About  1  cc.  of  water  is  then  carefully  dropped  on  the 
Siufaee,  which,  however,  it  does  not  actually  touch,  being  suspended 
by  a  blanket  of  steam.  The  hydrolysis  now  occurs  to  a  much  greater 
extent  than  in  water  solution.  This  is  due  in  the  first  place  to  the  high 
temperature,  and  in  the  second  place  to  the  fact  that  the  HC1  formed 
passes  up  into  the  drop  of  water,  away  from  the  scene  of  action.  It  is 
just  as  though  the  acid  were  non-ionized,  as  far  as  its  action  is  concerned. 
This  process  by  which  the  H+  ion  and  the  01  ~  ion  are  constantly 
removed,  thus  furthers  the  hydrolytic  action,  and  the  latter  would  go 
on  to  completion  if  the  water  lasted  long  enough.  In  any  case,  the 
residual  sodium  chloride  always  gives  an  alkaline  reaction  after  being 
thus  heated  in  contact  with  water. 

C  k.*Emich,  Ber.,  40,  1482  (1901). 


HYDROLYSIS  OF  SALTS  221 

(6)  Hydrolysis  of  the  salt  of  a  weak  acid  and  a  strong  base,  e.g., 
KCN  or  Na2CO3:  Potassium  cyanide  is  a  salt  of  KOH  and  HCN. 
When  it  is  dissolved  in  water,  the  important  equilibria  are  : 


±K+    +CN~ 
H2O    <=±OH~+H+ 

4T 

HCN 

HCN  is  a  very  weak  acid,  being  ionized  even  in  M/10  solution  only 
to  the  extent  of  0.0001  and  in  molar  solution  still  less,  of  course.  Potas- 
sium cyanide,  like  salts  in  general,  is  highly  ionized,  giving  a  concen- 
tration of  CN~  too  large  to  remain  in  equilibrium  with  even  the  extremely 
small  concentration  of  H+  present  from  the  water.  Therefore,  non- 
ionized  HCN  is  formed  until  the  proper  equilibrium  concentrations  are 
reached.  This,  of  course,  uses  up  CN~  and  H+,  and  more  KCN  and 
H2O  will  ionize  to  supply  the  deficiency  and  again  restore  their  own 
equilibria.  This  further  ionization  of  KCN  and  H2O  causes  an  accumu- 
lation of  K+  and  OH~  which  are  not  used  up  except  by  the  possible 
formation  of  a  trace  of  non-ionized  KOH.  Note  that  this  accumulation 
of  OH~  will  make  the  solution  alkaline  if  its  concentration  becomes 
large  enough.  In  this  particular  case  it  does  this  to  a  marked  degree. 
Note  also  that  the  alkalinity  is  due  to  the  OH~  and  not  to  KOH.  It  is 
a  common  mistake  to  say  that  hydrolysis  results  here  in  making  the 
solution  alkaline  "  because  KOH  is  formed."  It  would  be  nearer  right 
to  say  "  because  KOH  is  not  formed,"  for  the  OH  must  remain  in  the 
ionic  condition  if  it  is  to  affect  the  indicator. 

The  hydrolysis  of  sodium  carbonate  also  results  in  making  the  solu- 
tion of  that  salt  alkaline,  and  for  the  same  reason  as  in  the  case  just 
described.  The  following  equilibria  will  indicate  the  course  oi  the 
reaction  : 

Na2C03^2Na++C03= 


H2O        <=>  OH 

it 
HCO3" 

The  hydrolysis  in  this  case  does  not  go  so  far  as  to  cause  the  forma- 
tion of  anything  more  than  an  unmeasurable  trace  of  free  carbonic  acid, 
H2CO3,  but  it  does  cause  the  formation  of  the  bicarbonate  ion,  HC03~, 
which  is  much  less  highly  ionized.  (The  student  should  trace  out  the 
steps  in  this  process  and  carefully  write  them  down  in  the  best  possible 
form.) 


222  HOMOGENEOUS   EQUILIBRIUM 

(c)    Hydrolysis  of  the  salt  of  a  strong  acid  and  a  weak  base,  e.g., 
NH4CL—  The  acid  represented  here  is  HC1,  and  the  base  is  NH4OH. 
The  important  equilibria  are  : 


H20      + 

T4 

NH4OH 

The  results  here  are  perfectly  obvious:  NH4+  and  OH~,  will  unite  to 
form  NH4OH  (0.004  ionized  in  molar  solution),  and  the  ions  Cl~  and 
H+  will  accumulate  because  of  the  resulting  advance  of  the  upper 
reactions.  The  solution  will  therefore  give  an  acid  reaction  (not 
because  HC1  is  formed,  but  because  it  is  not  formed  except  in  possible 
traces.  NH4OH  is  the  substance  really  formed)  . 

(d)  Hydrolysis  of  the  salt  of  a  weak  acid  and  a  weak  base,  e.g.,  NH4CN, 
or  (NH4)2C03. 

The  equilibria  will  be  such  as  the  following: 


H20 

T4       4T 

NH4OH    HCN 

The  hydrolysis  into  the  corresponding  acid  and  base  will,  in  such  a  case 
as  this,  be  almost  complete.  This  is  due  to  the  fact  that  there  is  no 
chance  for  the  accumulation  of  any  of  the  ions.  According  to  Stieglitz,* 
a  salt  of  HCN  with  a  base  as  weak  as  this  acid  would  be  99.35  per  cent 
hydrolyzed  in  M/10  solution  at  25°. 

Degree  of  Hydrolysis  and  lonization  Constants.  —  By  "  degree  of 
hydrolysis  "  is  meant  the  fraction  or  per  cent  of  a  salt  hydrolyzed. 
Degree  of  hydrolysis  may  be  determined  in  several  ways,  of  which  we 
shall  discuss  only  two  : 

(a)  Degree  of  hydrolysis  may  be  calculated  from  the  ionization 
constant  of  the   weak  acid  or  base  represented  in  the  given  salt,  pro- 
vided the  degree  of  ionization  of  the  salt,  the  acid,  and  the  base,  and  the 
ionization  constant  for  water  are  known. 

(b)  The  degree  of  hydrolysis  may  be  calculated  from  the  concen- 
tration of  H+  or  OH~  found  in  the  solution,  together  with  the  known 
ionization  data  of  the  acid  or  base. 

*  Qualitative  Analysis,  Vol.  I,  p.  185  (1911). 


DEGREE  OF  HYDROLYSIS  AND  IONIZATION  CONSTANTS     223 

If  the  degree  of  hydrolysis  of  a  salt  is  known  (with  the  ionization 
data  and  the  constant  for  water)  the  ionization  constant  for  the  weak 
acid  or  base  can  be  calculated.  If,  on  the  other  hand,  the  degree  of 
hydrolysis  of  the  salt  and  the  ionization  constant  of  the  weak  acid  or 
base  are  known  (with  ionization  data)  the  constant  for  water  may  be 
calculated. 

Take  the  case  representing  a  strong  acid  and  a  weak  base,  using 
method  (a): 

Let  the  salt  be  represented  by  Me  Ac,  Me  representing  the  metal 
and  Ac  the  acid  radical.  The  equilibrium  relations  are  represented  as 
follows:  /V0-£ 

-  MeAc<=±Me++Ac- 

H2O    <=±OH~+H+ 

4T 

MeOH 

&t(oHb 

The  same  OH  is  competed  for  by  the  H+  to  form  water  and  by 
Me  to  form  the  weak  base  MeOH.  Two  equilibria  must  therefore  be 
simultaneously  satisfied :  ^  . 

m  (Me+)X(OH)_ 

(MeOH) 
and 

(2)  (H+)X(OH-)=ffw 

Dividing  (1)  by  (2),  we  eliminate  OH~,  and  then  have 


(MeOH)X(H+)      Kw 

The  concentration  of  the  ion,  (Me),  may  be  calculated  from  the 
concentration  of  the  unhydrolyzed  salt  by  multiplying  by  the  degree 
of  ionization,  a\\  and  (H+)  may  be  calculated  from  the  concentration 
of  the  strong  acid  formed,  by  multiplying  by  its  degree  of  ionization, 
0:2.* 

Substituting  these  values  in  (3),  we  have 

, ,  s  (unhydrolyzed  salt)  a\     _  K^se 

(MeOH)  X  (strong  acid)a2~  ~K^> 

*  a-z  is  given  the  value  corresponding  to  the  concentration  of  the  salt  whose 
degree  of  hydrolysis  is  being  calculated.  Although  the  acid  is  very  dilute  the  effect 
of  the  common  ion  from  the  salt  reduces  its  ionization  to  this  extent. 


224  HOMOGENEOUS  EQUILIBRIUM 

Again,  (unhydrolyzed  salt)  =  (total  salt)  —  x,  where  x  =  concentra- 
tion of  the  hydrolyzed  part;  x  also  equals  (strong  acid)  and  (weak  base) 
since  every  mole  of  salt  hydrolyzed  gives  1  moleeate-of  each.  We  may 
therefore  write 

[(total  salt)  —  x]  ai     Kbase 


(5) 


x2  a2  Kw 


Where  Kbase  is  greater  than  10  10,  x  will  be  very  small,  and  the  term 
[(total  salt)—  a:]  is  practically  the  same  as  (total  salt).  We  may  there- 
fore write  in  such  cases 

/cv  (total  salt)  ai     Kbase 

~~      =  ~ 


The  value  for  x  will,  as  stated,  represent  the  concentration  of  weak  base, 
(MeOH),  formed.  The  degree  of  hydrolysis  is  then  obtained  by  dividing 
this  by  the  total  concentration  of  the  salt. 

The  case  representing  a  weak  add  and  strong  base  involves  exactly 
the  same  sort  of  calculation  as  the  above.  The  only  difference  is  that 
here  it  is  the  H+  ion  which  is  competed  for,  and  we  finally  obtain 
equation  (4)  in  the  form 

(unhydrolyzed  salt)  «!    _K&cia 
(strong  base)  «2  X  (H  Ac)      Kw 

H  Ac  represents  the  weak  acid. 

The  final  form  of  the  equation  (equation  6')  will  be 

(total  salt)  a\     K&C{A 


(60 


X2 


<X2 


Method  (6)  is  very  simple:  We  determine  the  H+  concentration,  and 
from  this  the  concentration  of  acid  formed.  The  degree  of  hydrolysis 
then  equals  concentration  of  acid  formed  divided  by  concentration  of 
salt.  Thus,  in  M/10  aniline  chloride,  the  hydrogen  ion  concentration 
was  found  by  the  indicator  method  to  be  1.3  X  10~3.  The  ionization  of 
M/10  HC1  M  is  0.92.  The  total  concentration  of  HC1  formed  by 
hydrolysis  was  1.3  X  10~3/0.92,  or  1.4  X 10 ~3.  The  degree  of  hydrolysis, 
was  therefore  1.4X10~3/0.1,  or  1.4  per  cent. 

The  use  of  hydrolysis  data  for  calculating  an  ionization  constant  may 
be  illustrated  as  follows: 

We  may  calculate  the  ionization  constant  for  HCN  from  the  hydroly- 
sis data  of  M/10  KCN.  From  equation  (6')  above  we  obtain 

(total  salt)  «i  Kw 


KB.CIA  — 


X2  0.2 


BUFFER  SOLUTIONS  .     225 

The  degree  of  hydrolysis  of  M/10  KCN  at  20°  C.  is  1.3  per  cent,  x 
therefore  equals  1.3  per  cent  of  0.1,  or  0.0013.  «i  is  0.85,  «2  is  0.91, 
Kw  =  10~14.  Substituting  values,  we  have 

0.1X0.85X10-14  fr.ovlo_10 
K&cm=  (0.0013)2X0.91  '  ° 

Compare  this  value  with  the  constant  given  in  the  table,  page  208. 

Solutions  of  Constant  H+  and  OH~  Concentration.  ("Buffer 
Solutions."). — When  a  drop  of  normal  acid  is  added  to  a  liter  of  pure 
water,  the  hydrogen  ion  concentration  is  increased  two-hundred  fold. 
In  the  same  way,  when  a  drop  of  normal  alkali  is  added  to  a  liter  of  pure 
water,  the  hydroxyl  ion  concentration  is  increased  two-hundred  fold. 
This  simply  means  that  water  has  no  reserve  power  to  prevent  the 
change  of  its  H+/OH~  ratio.  We  have  said  that  the  concentrations  of 
H+  and  OH~  in  pure  water  at  20°  C.  are  10~7,  and  this  is  true;  but  it 
can  be  seen  from  the  above  that  slight  traces  of  impurity  will  greatly 
change  these  values.  Water  has  probably  never  been  made  so  pure 
that  the  concentrations  of  H+  and  OH~  are  exactly  10 ~7;  the  correct 
value  has  been  calculated.  Now  it  is  often  important  to  have  a  solution 
of  known  acidity  or  alkalinity  which  cannot  be  easily  changed,  and 
which  can  therefore  be  depended  on  to  protect  itself  against  outside 
influences.  Such  a  solution  can  be  made  up  by  simply  applying  the 
principles  we  have  been  stating. 

Any  solution  which  contains  a  weak  acid  along  with  its  salt  or  a 
weak  base  along  with  its  salt  has  just  this  power.  W  Take,  for  example,  a 
solution  of  acetic  acid  and  sodium  acetate.  Such  a  solution,  as  we  know, 
contains  a  high  concentration  of  non-ionized  acetic  acid  and  a  high  con- 
centration of  acetate  ion.  If  an  acid  is  added  to  this  solution  its  H+ 
ion  is  immediately  captured  by  the  acetate  ion  to  form  non-ionized 
acetic  acid.  If  an  alkali  is  added,  its  OH~  ion  combines  with  the  small 
amount  of  H+  ion  present,  to  form  water,  and  further  ionization  of  the 
acetic  acid  immediately  restores  the  old  value  for  the  H+  ion. 

If  we  desire  a  solution  to  have  the  same  reserve  power  for  the  neu- 
tralization of  either  H+  ion  or  OH~  ion,  we  must  evidently  have  present 
the  same  concentration  of  acid  ion  and  of  non-ionized  acid.  At  these 
concentrations  the  H+  ion  will  have  the  same  numerical  value  as  the 
ionization  constant  for  the  acid.  This  can  be  seen  from  the  equilibrium 
equation  for  acetic  acid. 

(H+)X(ae-) 
(Hac)       ' 


226  HOMOGENEOUS  EQUILIBRIUM 

If  (ac~)  equals  (H  ac)  these  factors  cancel  out,  and  we  then  have 
left  (H+)  =1.8X10-5.  From  this  we  see  that  the  condition  which 
could  be  maintained  best  with  acetic  acid  —  the  condition  where  (ac~) 
equals  (H  ac)  —  would  be  a  hydrogen  ion  concentration  equal  numer- 
ically to  the  constant  for  this  acid.  The  same  thing  is  true  in  any  case. 
Therefore,  if  we  wish  to  maintain  a  certain  acidity  (concentration  of 
H+  ion)  we  select  an  acid  whose  constant  comes  as  near  as  possible  to 
being  numerically  equal  to  the  given  concentration.  If  we  then  add 
the  amount  of  salt  necessary  to  give  the  desired  hydrogen  ion  concen- 
tration, we  have  a  buffer  solution  of  the  greatest  possible  efficiency. 

An  acid  salt  is  often  used  in  place  of  the  acid  itself.  Thus,  sodium 
dihydrogen  phosphate  is  a  favorite  for  this  purpose.  It  is  mixed  with 
the  di  sodium  salt. 

It  is  interesting  to  note  in  passing  that  the  blood  is  a  buffer  solution. 
It  contains  acid  phosphates  and  carbonates  which  accurately  maintain 
a  definite  acidity  (or  alkalinity  rather).  Experiments  on  dogs  have 
shown  that  an  animal  weighing  perhaps  15  kg.  is  able  to  correct  the 
acidity  produced  by  injecting  as  much  as  2  cc.  of  concentrated  hydro- 
chloric acid  into  the  blood  stream. 

EXERCISES 

1.  Develop  the  equilibrium  equations 


(A)X(B) 

I          = 


2.  Determine  the  constant  for  the  reaction  H2+I2<=^2HI,   at  440°  C.,  from 
Bodenstein's  data  (page  201). 

3.  How  is  the  value  of  an  equilibrium  constant  affected  by  change  in  the  con- 
centrations of  the  reacting  substances?     Proof? 

4.  How  would  change  of  temperature  affect  the  equilibrium  mentioned  in  (2)? 
What  is  the  general  rule  as  to  temperature  effects? 

6.  Mention  several  practical  ways  of  changing  the  concentrations  of  the  three 
reacting  substances  mentioned  in  (2)  and  show  just  how  such  changes  will  affect  the 
equilibrium. 

6.  Describe  examples  of  gaseous  equilibria  showing  the  effect  of  change  in  total 
pressure. 

7.  What  effect  has  a  catalyst  on  a  case  of  homogeneous  equilibrium? 

8.  Work  out  the  ionization  constant  for  acetic  acid  from  the  conductivity  data. 

9.  What  is  meant  by  saying  that  the  ionization  of  a  substance  does,  or  does  not, 
follow  the  equilibrium  law?     Examples. 

10.  By  use  of  the  table  of  ionization  constants,  determine  the  following: 
(a)  The  H+  ion  concentration  in  0.15  molar  acetic  acid. 

(6)  The  concentration  of  the  primary  H+  ion  in  0.1  molar  phosphoric  acid. 
(c)   The  concentration  of  OH~~  ion  in  0.5  molar  ammonium  hydroxide. 


EXERCISES  227 

11.  The  primary  hydrogen  of  molar  phosphoric  acid  has  been  neutralized  by 
means  of  NaOH,  the  solution  now  containing  only  molar  NaH2PO4.     This  salt  is 
60  per  cent  ionized  into  Na+  and  H2PO4~.  Find  the  concentration  of  the  H2PO4~ 
ion.     By  use  of  the  constant  for  the  secondary  ionization  of  phosphoric  acid,  find  also 
the  concentration  of  the  secondary  H+  ion  in  this  solution. 

12.  Name  and  describe  two  general  methods  of  displacing  ionic  equilibrium. 

13.  Work  out  the  quantitative  effect  of  adding  to  a  molar  solution  of  acetic  acid 
an  equivalent  amount  of  sodium  acetate. 

14.  Give  the  equilibrium  involved  and  work  out  the  quantitative  effect  of  adding 
to  a  molar  solution  of  hydrochloric  acid  an  equivalent  amount  of  sodium  acetate. 

15.  Explain  the  equilibrium  relations  involved  in  the  action  of  hydrochloric  acid 
on  sodium  carbonate. 

16.  Show  how  volatility  and  insolubility  may  enter  into  neutralization  reactions. 

17.  Show  by  examples  how  the  common  ion  effect  is  involved  in  the  titration  of 
weak  acids  and  bases. 

18.  Explain  the  equilibrium  relations  of  water,  including  temperature  effect. 

19.  Give  details  of  four  typical  cases  of  hydrolysis. 

20.  Develop  the  equation 

(total  salt)  «i  _  K  base 
*2«2  Ku 

for  determining  degree  of  hydrolysis.     What  is  x,  and  how  is  the  degree  of  hydrolysis 
determined  from  it? 

21.  Calculate  the  ionization  constant  for  acetic  acid  from  the  following  data: 
N/10  sodium  acetate  is  0.0066  per  cent  hydrolyzed  at  20°  C. 

The  unhydrolyzed  salt  is  79  per  cent  ionized.     N/10  NaOH  is  91  per  cent  ionized. 

22.  What  theoretical  considerations  are  involved  in  "buffer  solutions"?     Just 
how  are  they  prepared  for  the  greatest  efficiency?     Give  a  physiological  example. 


CHAPTER  XVII 
HETEROGENEOUS  EQUILIBRIUM 

Definition  of  Terms.  —  In  our  introduction  to  the  last  chapter  we 
mentioned  two  kinds  of  equilibrium.  One  of  these  was  the  equilibrium 
between  substances  mixed  together  in  homogeneous  fashion,  as,  for 
example,  a  mixture  of  gases  or  a  solution  containing  more  than  one 
substance.  The  other  kind  of  equilibrium  was  that  found  between 
substances  separated  from  each  other  by  distinct  boundary  lines,  as, 
for  example,  a  liquid  and  its  vapor,  or  a  solid  and  a  gas.  The  latter 
form  we  have  called  "  heterogeneous,"  simply  to  distinguish  it  from  the 
homogeneous  sort.  Heterogeneous  equilibrium  often  exists  between 
different  forms  of  the  same  substance,  as  between  water  and  vapor,  and 
is  then  a  purely  physical  condition.  It  may  also  include  those  cases 
where  the  members  taking  part  are  different  substances.  An  example 
of  the  latter  sort  is  the  equilibrium  between  calcium  carbonate  and 
the  products  of  its  decomposition,  carbon  dioxide  and  calcium  oxide. 
This  is  a  truly  chemical  equilibrium,  although  heterogeneous. 

Physical  Equilibrium.  —  Heterogeneous  equilibrium  is  governed  by 
the  same  factors  as  those  governing,  homogeneous  equilibrium.  These 
are  concentration,  temperature,  and  pressure.  For  this  reason  it  needs 
no  very  special  treatment.  This  is  particularly  true  of  those  cases  where 
the  change  involved  is  chemical.  For  the  sake  of  clearness  we  may, 
however,  show  how  the  ordinary  laws  work  out  in  those  cases  where  the 
change  is  purely  physical. 

The  law  of  physical  equilibrium  holds  that  when  the  same  sub- 
stance is  present  in  two  physical  states,  or  phases,  in  equilibrium  with 
each  other,  as  AI  ±+  A2,  the  concentrations  of  the  substances  in  the  two 
states  bear  to  each  other  a  constant  ratio,  thus  : 


That  this  is  true  has  been  proved  again  and  again  experimentally, 
but  its  reasonableness  may  also  be  shown,  as  in  the  case  of  chemical 
equilibrium.  The  forward  reaction,  A\—  >  ^2,  proceeds  at  a  certain 

228 


THE  LAW  OF  PARTITION  229 

speed,  which  is  proportional  to  the  concentration  of  AI.     We  may 
therefore  say,  as  before,  that 


where  Si  is  the  speed  in  moles  per  second,  and  K\  is  the  speed  constant. 
In  the  same  way  we  may  write  for  the  reverse  reaction  : 

(A2)XK2=S2 
When  the  two  reactions  are  in  equilibrium,  Si  =  S2)  and  therefore 

(Al)XKi  =  (A2)XK2 
From  this 


As  in  the  case  of  chemical  equilibrium,  the  equilibrium  ratio,  and 
hence  the  value  of  K,  are  independent  of  concentration;  that  is,  we 
get  the  same  value  for  K  whether  the  concentrations  (Ai)  and  (4  2)  are 
large  or  small.  The  only  factor  which  can,  in  general,  change  this  value 
is  a  change  in  temperature. 

In  the  succeeding  paragraphs  we  shall  discuss  examples  of  hetero- 
geneous equilibrium,  both  chemical  and  physical. 

The  Law  of  Partition.  —  If  we  place  two  non-miscible  solvents  in 
contact,  and  then  add  a  substance  which  is  soluble  in  both,  this  sub- 
stance will  so  distribute  itself  that  the  ratio  between  its  concentrations 
in  the  two  solvents  is  a  constant.  This  is  called  the  principle  of 
"  partition,"  and  is  a  case  of  physical  equilibrium. 

An  example  of  partition  is  the  distribution  of  succinic  acid  between 
water  and  ether.  A  water  solution  of  succinic  acid  is  placed  in  a  bottle, 
ether  is  added,  and  the  mixture  is  then  shaken.  The  acid  distributes 
itself  between  the  two  solvents  until  equilibrium  is  reached.  When 
the  mixture  is  allowed  to  stand,  the  two  solvents  carrying  the  acid 
separate  into  distinct  layers,  the  ether  layer  at  the  top.  A  known  vol- 
ume of  each  layer  may  then  be  withdrawn  with  a  pipette  and  titrated 
separately  with  an  alkali.  Since  equal  volumes  of  the  two  solutions 
have  been  used,  the  number  of  cubic  centimeters  of  alkali  required  in 
each  case  may  be  regarded  as  a  measure  of  the  concentration.  The 
ratio  between  the  concentrations  in  the  two  layers  may  then  be  cal- 
culated at  once.  As  stated  above,  this  ratio  will  always  prove  to  be 
the  same  if  the  same  temperature  is  used,  no  matter  what  the  total 
concentrations  may  happen  to  be.  At  22°  C.,  this  ratio  stated  as 
(Cwater)/  (Cotter),  is  not  far  from  7. 

Another  example  is  the  distribution  of  bromine  between  water  and 
carbon  tetrachloride.  This  experiment  is  carried  out  in  almost  the 


230  HETEROGENEOUS  EQUILIBRIUM 

same  way  as  with  succinic  acid,  except  that  the  concentration  of  bro- 
mine is  determined  by  adding  a  known  volume  of  one  layer  to  an  excess 
of  potassium  iodide  solution,  displacing  an  equivalent  amount  of  iodine, 
which  is  then  titrated  with  sodium  thiosulphate.  Here  again,  the  ratio 
between  the  concentrations  in  the  two  layers  is  found  to  be  independent 
of  their  numerical  values. 

It  is  the  principle  of  partition  which  underlies  such  processes  as 
ether  extraction.  We  have  a  small  amount  of  some  substance  dissolved 
in  water,  for  example,  and  wish  to  remove  it.  We  add  some  non- 
miscible  solvent  in  which  the  substance  is  more  soluble,  and  shake  to 
insure  good  contact.  The  substance  dissolves  in  the  second  solvent 
until  the  ratio  between  its  concentration  in  this  solvent  and  in  the  water 
reaches  the  constant  value.  We  allow  the  two  liquids  to  separate  and 
then  draw  off  the  one  lying  underneath.  If  we  repeat  the  process  with 
another  portion  of  the  second  solvent  the  concentrations  in  the  two 
solvents  will  this  time  be  much  smaller,  but  the  ratio  between  them  will 
be  the  same  (if,  of  course,  we  keep  them  in  contact  until  equilibrium  is 
reached) .  We  can  thus  remove  by  this  method  a  very  large  proportion 
of  the  dissolved  substance.  We  can  never  remove  it  all,  however,  for 
at  the  last  extraction,  no  matter  how  many  have  been  made,  the  equi- 
librium between  concentrations  is  bound  to  be  encountered. 

Another  common  example,  showing  the  use  of  this  principle,  is  the 
matter  of  testing  for  the  free  halogens.  Bromine  or  iodine  is  set  free 
by  chlorine  in  water  solution,  and  then  extracted  by  shaking  with  chloro- 
form. As  the  halogens  are  more  soluble  in  this  solvent,  we  can  use  a  very 
small  amount  of  it,  and  thus  get  a  concentrated  solution  whose  color  is 
easily  visible.  However,  even  in  this  case,  we  are  only  extracting  a 
portion  of  the  halogen,  for  we  meet,  as  in  the  case  above,  the  same  law 
of  equilibrium,  when  the  ratio  between  the  concentrations  in  the  two 
solvents  reaches  some  constant  value. 

Vapor  Pressure  of  Hydrates. — We  are  all  familiar  with  such 
hydrated  compounds  as  CuSO4-5H2O  or  MgCl2  •  6H2O,  all  of  which 
go  under  the  general  name  of  "  hydrates."  These  compounds  are  not  to 
be  confused  with  hydroxides,  for  they  do  not  neutralize  acids  (except 
in  the  case  of  salts  of  very  weak  acids,  such  as  sodium  carbonate,  which 
do  so  for  a  very  different  reason,  as  already  discussed).  About  the 
middle  of  the  last  century  hydroxides  were  thought  to  be  hydrated 
oxides  (e.g.,  Na20-H2O)  and  were  called  "  hydrates."  This  nomen- 
clature still  clings  to  the  language  of  pharmacy,  where  we  find  such 
terms  as  "  sodium  hydrate  "  or  "  hydrate  of  soda." 

It  should  be  noted  that  the  water  contained  in  a  hydrate  is  a  funda- 
mental part  of  it,  not  merely  water  attached  to  the  surface  or  enclosed 


VAPOR   PRESSURE  OF  HYDRATES  231 

in  the  crystals.  This  is  shown  by  the  fact  that  the  amount  of  water 
attached  to  a  mole  of  an  anhydrous  compound  can  always  be  stated  as  a 
definite  number  of  moles  of  water.  Moreover,  the  hydrates  always 
possess  properties  not  possessed  by  the  anhydrous  compounds.  Thus 
the  hydrate  CuSO4-5HoO  is  blue  in  color  and  crystallizes  in  triclinic 
prisms,  while  the  anhydrous  salt  is  white  and  crystallizes  in  fine  needles. 

The  amount  of  water  held  by  different  substances  (the  degree  of 
hydration)  is  quite  variable.  Some  crystals,  like  sodium  chloride, 
ordinarily  contain  no  water  of  hydration,  and  are  spoken  of  as  "  anhy- 
drous." Copper  sulphate  forms  three  hydrates,  CuSCU-SH^O,  CuSCU- 
3H20,  and  CuSCU-H^O,  the  pentahydrate  being  the  most  common. 
Sodium  carbonate  forms  a  decahydrate  if  crystallized  at  room  tem- 
perature, and  a  monohydrate  if  the  crystallization  occurs  above 
35.1°  C.  Sodium  sulphate  gives  a  heptahydrate  and  a  decahydrate, 
and  above  32.4°  C.  is  anhydrous. 

But  for  us  in  this  study  the  most  important  characteristic  of  hydrates 
is  the  fact  that  they  tend  under  one  set  of  conditions  of  temperature  and 
humidity  to  dissociate  into  less  hydrated  forms,  and  under  another  set  of 
conditions  to  become  more  highly  hydrated,  and  in  so  doing  to  maintain 
certain  equilibrium  relations  with  the  vapor  of  the  surrounding  atmos- 
phere. Just  what  these  equilibrium  relations  are  can  be  shown  by  use 
of  the  following  example:  If  a  sample  of  copper  sulphate  pentahydrate 
is  mixed  with  one  of  its  lower  hydrates  or  with  the  anhydrous  salt, 
and  placed  in  a  closed  vessel  free  from  moisture  and  at  a  definite  tem- 
perature, water  vapor  will  be  given  off  just  as  it  is  from  liquid  water. 
After  a  time,  when  the  vapor  reaches  a  certain  definite  pressure,  the 
process  seems  to  stop,  and  from  that  time  on  we  find  the  two  solid  phases 
in  equilibrium  with  the  vapor.  If  we  increase  the  concentration  of  the 
vapor,  more  of  it  unites  with  the  lower  hydrate  to  fcrm  the  higher;  if 
we  decrease  the  concentration  of  the  vapor,  more  of  the  higher  hydrate 
dissociates;  but  in  either  case  the  former  state  of  equilibrium  is  restored. 

The  vapor  pressure  thus  in  equilibrium  with  the  two  solid  phases  is 
ordinarily  spoken  of  as  the  vapor  pressure  of  the  higher  hydrate.  Thus, 
the  pressure  in  equilibrium  with  a  mixture  of  the  5  and  3  hydrates  of 
of  CuSCU  is  called  the  vapor  pressure  of  the  5  hydrate.  It  is  important 
to  note  here  that  the  presence  of  the  second  solid  phase  is  necessary; 
without  this  a  hydrate  gives  no  definite  vapor  pressure.  The  choice  of 
the  second  solid  phase  is  also  important,  for  the  vapor  pressure  varies 
according  to  the  phase  into  which  dissociation  occurs.*  The  second  phase 
may,  of  course,  appear  spontaneously,  but  it  does  not  always  do  so.  f 

*  Roozebqom,  Zeitschr.  physikal.  Chemie,  4,  43. 

f  Perfect  crystals  of  a  single  hydrate  will  sometimes  remain  indefinitely  without 


232  HETEROGENEOUS  EQUILIBRIUM 

Whether  a  hydrate  will,  under  any  given  conditions,  gain  or  lose 
water,  can  now  be  seen  to  depend  on  the  relation  between  its  vapor 
pressure  and  the  pressure  of  the  water  vapor  (humidity)  of  the  sur- 
rounding atmosphere.  If  the  vapor  pressure  of  the  hydrate  and  that 
of  the  atmosphere  surrounding  it  are  the  same,  the  rates  at  which  water 
will  be  released  and  recombined  will  be  equal,  and  the  hydrate  will 
neither  gain  nor  lose  water.  If  the  humidity  of  the  surrounding  atmos- 
phere is  less  than  the  vapor  pressure  of  the  hydrate,  the  latter  will  (in 
the  presence  of  a  lower  hydrate)  lose  water.  When  a  hydrate  thus  gives 
off  water  under  ordinary  atmospheric  conditions  it  is  said  to  " effloresce." 
The  decahydrates  of  sodium  sulphate  and  sodium  carbonate  do  this 
practically  always,  because  their  vapor  pressures  are  usually  higher 
than  those  in  the  air.  Copper  sulphate  pentahydrate  may  or  may  not 
do  this.  Thus,  if  the  atmosphere  is  half  saturated  with  water  vapor  at 
25°  C.  the  water  vapor  in  it  has  a  pressure  of  11.8  mm.  At  this  tem- 
perature the  pentahydrate  (with  the  trihydrate)  has  a  vapor  pressure  of 
7.8  mm.*  Under  these  conditions  it  will,  therefore,  not  effloresce.  If, 
however,  the  humidity  of  the  air  were  only  30  per  cent  (7.08  mm.), 
the  pentahydrate  would  effloresce. 

As  would  be  inferred  from  the  above  discussion,  the  vapor  pressures 
of  hydrates,  like  that  of  pure  water,  are  functions  of  the  temperature. 
To  illustrate  this  we  present  the  curves  of  Fig.  29,  which  show  the 
change  in  vapor  pressures  of  the  hydrates  of  copper  sulphate  with  change 
in  temperature. 

It  will  be  noted  that  at  50°  C.  the  vapor  pressures  of  the  5,  3,  and  1 
hydrates  are,  respectively,  47  mm.,  30  mm.,  and  4.4  mm.  From  this 
it  is  evident  that  at  50°,  under  ordinary  atmospheric  conditions  of 
humidity,  the  first  two  hydrates  would  be  decomposed,  but  the  mono- 
hydrate  would  be  left  because  its  vapor  pressure  is  less  than  the  humid- 
ity is  likely  to  be.  Even  at  100°  C.  the  monohydrate  is  not  usually 
decomposed.  Note  also  the  reverse  process:  If  anhydrous  copper  sul- 
phate is  put  into  an  atmosphere  (at  50°  C.)  where  the  humidity  is  equal 
to  or  greater  than  4.4  mm.,  the  monohydrate  is  formed.  Where  the 
humidity  is  as  high  as  30  mm.  the  trihydrate  is  formed,  f 

dissociation,  even  where  the  humidity  is  very  low;  but  the  process  begins  at  once  on 
addition  of  a  trace  of  the  lower  hydrate.  This  is  called  "  suspended  transformation  " 
and  reminds  one  of  supersaturation.  (See  Phase  Rule,  p.  237.) 

*  R.  E.  Wilson,  Jour.  Am.  Chem.  Soc.,  43,  722.  This  paper  and  the  succeeding 
one  (by  A.  A.  Noyes)  give  accurate  methods  for  determining  the  vapor  pressure  of 
hydrate  mixtures. 

t  It  is  possible  also  to  cause  the  formation  of  the  monohydrate  here  as  an 
intermediate  product  by  inoculating  with  this  phase.  In  fact  it  will  probably  be 
formed  spontaneously, 


DESICCATION   BY  MEANS  OF  ANHYDROUS  SALTS 


233 


It  is  very  important  to  note  that  degrees  of  humidity  indicated  by 
points  between  the  hydrate  curves  of  any  given  salt  can  accomplish 
no  more  than  those  on  the  curve  immediately  below.  Thus,  humidities 
between  4.4  mm.  and  30  mm.  (say  25  mm.)  can  do  no  more  towards  the 
hydration  of  copper  sulphate  than  one  which  barely  equals  3.4  mm. 
This  means  that  the  monohydrate  of  copper  sulphate  can  remain  in 
contact  with  any  humidity  between  4.4  mm.  and  30  mm.  without 
taking  on  any  water.  The  same  thing  is  true  of  the  other  forms;  the 
anhydrous  form,  for  example,  will  not  take  on  water  (at  50°)  unless  the 
humidity  is  as  high  as  4.4  mm. 


0          10°    20U    30°     40°    50°     60°     70°    80°    90°    100° 
Temperature 

FIG.  29. — Vapor  Pressure  Curves  of  the  Hydrates  of  Copper  Sulphate. 

Desiccation  by  Means  of  Anhydrous  or  Partially  Hydrated  Salts.— 
The  process  of  desiccation  by  means  of  anhydrous  or  partially  hydrated 
salts  depends  almost  entirely  on  the  principles  just  described.  Thus, 
calcium  chloride,  one  of  the  commonest  desiccating  agents,  forms  sev- 
eral hydrates,  namely  1,  2,  4,  and  6.  The  vapor  pressures  given  by 
these  at  25°  C.  are  as  follows,  the  phases  present  being  indicated  in  each 
case: 

1.  (CaCl2  +CaCl2-H2O)  0.34mm.* 

2.  (CalCl2  •  H2O  +  CaCl2  •  2H2O)  0.54  mm. 
4.  (CaCl2-2H2O  +  CaCl2-4H2O)t  3.40  mm.  t 
6.  (CaCl2-4H2O+CaCl2-6H20)  5.08  mm.J 

*  Baxter  and  Starkweather,  Jour.  Am.  Chem.  Soc.,  38,  2038. 
t  The-  tetrahydrate  exists  in  two  forms,  designated  by  Roozeboom  (loc.  tit.) 
as  a  and  ft.    We  consider  only  the  a  form,  which  is  the  more  stable, 
t  Roozeboom,  loc.  cit. 


234  HETEROGENEOUS  EQUILIBRIUM 

When,  therefore,  any  one  of  the  mixtures  represented  in  this 
table  is  placed  in  a  moist  atmosphere,  it  is  quite  evident  from  our  pre- 
vious discussion  just  what  will  happen.  Ordinary  so-called  "  anhy- 
drous "  calcium  chloride  is  a  porous,  granular  mass  corresponding  at  its 
best  to  the  first  mixture  (CaCk-CaCk  •  EbO) .  If  a  gas  containing 
moisture  in  excess  of  0.34  mm.  pressure  is  conducted  very  slowly  over  a 
long  column  of  "  anhydrous  "  calcium  chloride  at  25°  C.,  the  humidity 
of  the  gas  will  at  first  be  reduced  to  0.34  mm.  After  a  time  the  anhy- 
drous salt  will  all  be  changed  to  monohydrate,  and  then  (if  the  entering 
gas  is  sufficiently  moist)  the  dihydrate  will  begin  to  be  formed.  We 
then  have  the  second  mixture  represented  in  the  table  (CaCk-H^O- 
CaCl2-2H2O),  whose  vapor  pressure  (at  25°)  is  about  0.54  mm.,  and 
the  humidity  of  the  issuing  gas  will  suddenly  rise  from  0.34  mm.  to 
0.54  mm.  And  so  the  process  will  go  on  in  steps,  giving  next  the  4-2 
mixture  with  a  vapor  pressure  of  3.4  mm.,  and  then  the  6-4  mixture 
with  a  vapor  pressure  of  5  mm.,  the  humidity  of  the  issuing  gas  being 
raised  accordingly.  Finally  a  solution  of  calcium  chloride  will  be 
formed,  having  various  vapor  pressures  depending  upon  the  concen- 
tration. 

All  this  presupposes  that  the  gas  which  is  to  be  dried  is  run  over  the 
calcium  chloride  so  slowly  that  equilibrium  can  really  be  established. 
It  is  quite  possible,  of  course,  to  conduct  the  gas  so  rapidly  that  equi- 
librium has  not  time  to  adjust  itself.  In  this  case  the  drying  would  be 
much  less  complete.  It  also  presupposes  that  the  drying  agent  is  in 
fairly  small  granules,  so  as  to  present  a  large  surface,  and  that  it  is  packed 
closely  in  the  tube.  It  is  important  to  note  also  that  the  successive 
stages  of  hydration  do  not  occur  uniformly  throughout  the  tube.  At 
the  end  of  the  column  where  the  gas  enters,  the  salt  will  go  rapidly 
through  all  the  stages  of  hydration,  even  to  the  formation  of  a  solution, 
and  this  condition  will  extend  slowly  through  the  whole  column.  The 
process,  however,  takes  a  considerable  length  of  time,  and  as  long  as  the 
main  part  of  the  salt  mixture  appears  dry  the  final  condition  is  remote. 
It  may  be  worth  noting  that  a  liter  of  gas  saturated  with  water  vapor 
at  25°  C.  contains  about  0.025  gm.  of  water.  From  this  it  is  possible 
to  make  a  rough  calculation  of  the  degree  of  hydration  reached  in  any 
mixture  and  thus  to  know  something  about  the  efficiency  of  the  drying. 
It  may  not  be  out  of  place  also  to  mention  the  mistake  often  made  in  the 
drying  of  gases,  namely  that  of  reversing  the  drying  tube.  If  a  tube  is 
used  in  one  direction  at  one  time  and  the  next  time  reversed,  the  highly 
hydrated  material,  formerly  at  the  entrance,  will  be  at  the  exit,  and  the 
humidity  of  the  issuing  gas  will  correspond  with  the  vapor  pressure  of 
this  material,  no  matter  how  efficient  the  rest  of  the  material  may  be. 


EQUILIBRIUM    RELATIONS   OF   WATER  235 

Nothing  but  a  thorough  knowledge  of  the  theory  of  hydrates  can  make 
apparent  the  stupidity  of  such  a  mistake.  Another  extremely  important 
point  connected  with  the  use  of  salt  hydrate  mixtures  as  drying  agents 
is  the  matter  of  temperature.  If  a  drying  column  containing  such  a 
mixture  is  used  it  will  do  its  most  effective  work  at  low  temperature 
where  the  vapor  pressure  of  the  hydrates  formed  is  very  low.*  Also, 
in  drying  liquids  by  putting  the  hydrate  mixtures  in  them  the  most 
effective  work  can  be  done  at  low  temperatures.  This  means  that 
it  is  not  permissible  to  dry  a  liquid  of  high  boiling-point  with  calcium 
chloride  and  then  distill  it  off  without  removing  the  drying  agent.  At 
the  necessary  temperature  it  is  quite  possible  that  the  aqueous  tension 
of  the  hydrated  drying  agent  might  be  so  high  that  the  distillate  would 
contain  more  water  than  did  the  original  liquid. 

Before  leaving  this  subject  it  should  be  mentioned  that  a  part  of  the 
drying  effected  by  anhydrous  salts  is  undoubtedly  due  to  a  cause 
entirely  foreign  to  the  matter  of  hydration,  namely  adsorption.  The 
researches  of  A.  T.  McPhersonf  show  that  granular  calcium  chloride 
which  has  been  heated  to  275°  (not  fused)  has  a  very  porous,  powdery- 
surface  which  is  capable  of  removing  water  down  to  a  pressure  which  is 
far  below  that  called  for  by  the  monohydrate.  The  water  is  simply 
condensed  around  the  minute  granules.  It  is  found  also  that  other 
fine  powders,  for  example  AbOs,  are  able  to  do  the  same  thing. 

Equilibrium  Relations  of  Water. — In  our  study  of  change  of  state 
(Chapter  III),  we  pointed  out  some  of  the  equilibrium  relations  between 
the  different  phases  of  water.  We  can  now  bring  this  material  together 
and  possibly  extend  it  somewhat  in  the  light  of  the  equilibrium  law. 

Water  may  exist  in  three  phases — solid,  liquid,  and  vapor.  In  dif- 
ferent cases  we  may  have  one  phase  present,  or  two  phases,  or  all  three ; 
but  in  any  case  where  two  or  more  phases  remain  together  permanently 
we  may  be  sure  they  are  existing  under  equilibrium  conditions.  The 
factors  involved  in  these  equilibrium  conditions  are  two,  namely, 
temperature  and  pressure.  The  curves  of  Fig.  30  will  help  us  to  make 
the  discussion  clearer. 

In  our  study  of  the  vapor  pressure  of  water  we  gave  a  table  represent- 
ing the  pressure  of  saturated  water  vapor  over  a  considerable  range  of 
temperature.  If  these  values  were  plotted  we  should  obtain  a  curve 
like  O'A.  At  0°  C.  the  pressure  is  4.6  mm.  At  higher  temperatures  the 
pressure  is  higher,  but  all  the  values  fall  on  the  line  OA.  Points  on  this 
line  therefore  represent  the  pressures  and  temperatures,  and  the  only 
ones,  at  which  water  and  its  vapor  can  exist  together  permanently.  If 

*  See  Baxter  and  Starkweather,  loc.  cit. 
f  Jour.  Am.  Chem.  Soc.,  39,  1317. 


236 


HETEROGENEOUS  EQUILIBRIUM 


a  pressure  is  maintained  which  is  above  this  line,  all  the  vapor  will  be 
condensed  to  liquid,  thus  destroying  the  vapor  phase.  If  a  pressure 
is  maintained  which  is  below  this  line,  all  the  liquid  evaporates,  thus 
destroying  the  liquid  phase.  We  may  change  the  pressure  if  we  allow 
the  temperature  to  be  changed  to  correspond,  or  we  may  change  the 
temperature  if  we  allow  the  pressure  to  change  to  correspond,  but  we 
may  not  change  more  than  one  at  once  to  suit  our  fancy. 

We  have  mentioned  the  fact  that  ice  possesses  a  vapor  pressure  as 
truly  as  does  water.  If  in  this  case  also  we  determine  the  values  for 
the  vapor  pressures  of  ice,  below  0°  C.,  and  plot  these  values  against  the 


Temperature 

FIG.  30. — Vapor  Pressure  and  Freezing-point  Curves  for  Water. 

• 

temperatures,  we  obtain  the  curve  OC.  Note  that  this  curve  is  not 
continuous  with  OA,  for  the  pressures  are  lower  than  -those  for  water 
would  be  for  the  corresponding  temperatures.  (See  OA'.}  Note 
also  that  the  curves  OA  and  OC  meet  at  0  where  the  vapor  pressures  of 
ice  and  water  are  equal.  Remember  that  the  line  OC  represents  the 
only  temperatures  and  pressures  at  which  ice  and  water  vapor  can 
exist  together  permanently.  Any  attempt  to  change  these  conditions 
to  points  not  on  this  line  will  certainly  result  in  the  complete  disap- 
pearance of  one  phase  or  the  other.  Note  finally  that  here  again,  as  in 
the  previous  case,  we  may  change  one  of  the  conditions  (temperature  or 
pressure)  if  we  allow  the  other  to  be  changed  to  correspond;  we  cannot 
change  more  than  one  at  will. 

Water  freezes  at  0°  C.  if  the  pressure  is  one  atmosphere.  If  the 
pressure  is  made  more  than  this  the  freezing  point  is  slightly  lowered  to 
correspond.  Plotting  freezing  points  against  pressures,  we  obtain  the 
curve  OB.  This  curve  represents,  therefore,  the  equilibrium  between 


THE   PHASE  RULE  237 

water  and  ice.  It  is  only  at  temperatures  and  pressures  on  this  line 
that  the  two  phases  can  exist  together  without  the  ultimate  disap- 
pearance of  one  phase.  Note  that  the  curve  slopes  slightly  back  towards 
the  vertical  axis,  because  higher  pressures  are  attended  by  slightly  lower 
freezing-points. 

The  point  0 — the  meeting-point  of  all  the  curves — is  called  the 
"  triple  point."  At  this  point  the  three  phases,  water,  ice,  and  vapor, 
can  exist  together  indefinitely.  Any  attempt  to  change  the  conditions 
of  temperature  or  pressure  represented  by  the  triple-point  will  result 
in  the  disappearance  of  one  or  more  phases.  Thus,  if  the  temperature 
is  raised  all  the  ice  will  melt.  If  the  pressure  is  increased  all  the  vapor 
will  condense.  This  system,  therefore,  allows  no  freedom  in  changing 
conditions. 

It  is  interesting  to  note  that  the  triple  point  is  not  quite  coincident 
with  what  we  call  the  freezing-point  of  water.  Water  freezes  at  0°  C. 
when  the  pressure  is  one  atmosphere.  At  the  triple  point  it  is  under 
pressure  of  only  4.6  mm.  (the  pressure  of  its  own  vapor).  Since  decrease 
in  pressure  raises  the  melting-point  it  is  evident  that  the  triple  point  will 
be  slightly  above  0°  C.  The  actual  value  is  0.007°. 

The  dotted  line  OA' ',  continuous  with  OA,  represents  the  fact  that 
it  is  possible  under  certain  conditions  to  lower  the  temperature  of  water 
below  0°  C.  without  its  actually  freezing.  The  line  also  represents  the 
vapor  pressure  curve  under  such  conditions.  The  state  here  represented 
is  metastable,  like  that  of  a  supersaturated  solution,  and  is  instantly 
upset  by  a  trace  of  solid. 

Out  in  the  regions  represented  by  the  free  areas  away  from  the  curves 
on  the  diagram,  only  a  single  phase  exists,  as,  for  example,  unsaturated 
vapor,  or  liquid  water.  Here  both  temperature  and  pressure  can  be 
varied  widely  at  once  without  destruction  of  phase. 

The  Phase  Rule. — After  a  careful  study  of  such  cases  of  equilibrium 
as  we  have  been  describing  and  many  others,  Willard  Gibbs,*  the 
American  physicist,  developed  in  1874  a  system  of  classification  which 
has  since  been  named  the  "  phase  rule."  Being  a  mathematical  physi- 
cist, Gibbs  stated  his  classification  in  terms  of  abstract  mathematics, 
and  for  thirteen  years  the  fine  generalizations  he  had  made  remained 
hidden  under  this  garb.  Finally,  in  1887,  Roozeboom  f  cleared  away 
the  mathematics  and  made  the  work  accessible  to  the  general  worker. 
Since  then  it  has  been  one  of  the  most  powerful  instruments  available 
for  the  solution  of  chemical  problems. 

*  Professor  of  Physics  in  Yale  University  (1839-1903). 

f  Hendrik  W.  B.  Roozeboom  (1854-1907),  Professor  of  Chemistry,  University  of 
Amsterdam. 


238  HETEROGENEOUS  EQUILIBRIUM 

Gibbs'  rule  holds  that  the  composition  of  a  system  in  equilibrium 
should  be  stated  in  terms  of  the  number  of  independent  constituents, 
which  he  calls  "  components"  He  then  shows  that  the  freedom  one  has 
to  change  the  conditions  of  temperature,  pressure,  or  concentration 
without  destro3?ing  a  phase  depends  on  the  relation  between  the  number 
of  components  and  the  number  of  phases.  From  these  relations  he  is 
able  to  deduce  many  important  and  otherwise  inaccessible  facts  concern- 
ing systems  in  equilibrium.  We  must  first  try  to  define  the  necessary 
terms : 

(a)  Phase. — We  have  shown  that  heterogeneous  equilibrium  deals 
with  bodies  which  are  separated  from  each  other  by  distinct  boundary 
lines.     These  physically   distinct   bodies   are  called   "  phases."     In   the 
mixture  of  ice,  water,  and  vapor  we  have  three  phases — solid,  liquid, 
and  gaseous — which,   although  in   contact,   are  separated  from  each 
other  in  just  this  way.     Their  boundary  lines  can  be  seen,  and  they  can 
be  separated  by  mechanical  means.     A  mixture  of  solid  and  solution 
consists  of  two  phases,  solid  and  liquid.     A  mixture  of  calcium  car- 
bonate, calcium  oxide,  and  carbon  dioxide  consists  of  three  phases,  two 
solid  and  one  gaseous. 

(b)  Component. — By  component  is  meant  one  of  the  fundamental 
units  which  are  necessary  for  the  building  up  of  a  system.     In  the  system 
water — ice — vapor,  there  is  only  one  component,  namely  water.     In  the 
system  CaCOs— CaO — CO2,  there  are  two  components,  namely  CaO 
and  CO2.     The  phase  CaCOs  is  not  to  be  regarded  as  a  component 
because  it  may  itself  be  built  up  from  the  other  two  compounds.     In 
the  case  of  an  aqueous  solution  of  a  salt  there  are  two  components,  salt 
and  water.     In  a  case  of  partition  of  a  solute  between  two  solvents, 
there  are  three  components,  the  two  solvents  and  the  solute.     In  the 
case  of  a  salt  hydrate  there  are  two  components,  the  anhydrous  salt  and 
water. 

(c)  Degrees  of  Freedom. — The  necessary  conditions  of  equilibrium, — 
temperature,  pressure,  and    concentration — are  spoken    of  as  '  inde- 
pendent variables";  but,  as  we  have  seen  above,  it  is  often  impossible  to 
vary  the  conditions  all  at  once  without  destroying  a  phase.  The  number  of 
such  changes  which  may  in  any  case  be  made  at  once  without  destroying  a 
phase  is  spoken  of  as  the  "  degrees  of  freedom."     In  the  system  water-vapor, 
we  may  change  only  one  condition  at  a  time.     For  example,  we  may 
change  the  temperature.     It  is  true  that  another  condition,  pressure, 
changes  at  the  same  time,  but  we  have  no  control  over  it;  we  can  only 
control  one  condition.     This  system  therefore  offers  only  one  degree  of 
freedom.     In  the  system  vapor,  we  may  change  both  temperature  and 
pressure  without  destruction  of  phase.     This  system  therefore  offers 


APPLICATIONS  OF  THE   PHASE  RULE  239 

two  degrees  of  freedom.  In  the  system  water-ice-vapor,  we  cannot 
change  any  condition  without  destroying  a  phase.  This  system  there- 
fore offers  no  degrees  of  freedom. 

A  system  which  offers  one  degree  of  freedom  is  usually  spoken  of  as 
"  uni  variant  ";  one  which  offers  two,  as  "  di  variant";  and  one  which 
offers  three,  as  "  tri variant ";  while  a  system  which  offers  none  is  called 
"  non- variant." 

From  the  examples  given  we  can  now  deduce  some  generaliza- 
tions : 

(1)  Where  a  system  has  one  component  and  three  phases  (water- 
ice-vapor),  or  two  components  and  four  phases,  etc.,  it  is  non-variant. 
From  this  we  conclude  that  when  the  number  of  phases  exceeds  the 
number  of  components  by  two  the  system  is  non-variant.  (2)  Where  a 
system  has  one  component  and  two  phases  (water-vapor),  or  two  com- 
ponents and  three  phases  (CaO — CCb — CaCOs),  etc.,  it  is  univariant. 
From  this  we  conclude  that  when  the  number  of  phases  exceeds  the 
number  of  components  by  one  the  system  is  univariant.  (3)  When  a 
system  has  one  component  and  one  phase  (vapor),  or  two  components 
and  two  phases  (gas-solution),  etc.,  it  is  di variant.  From  this  we  con- 
clude that  when  the  number  of  phases  equals  the  number  of  components 
the  system  is  divariant. 

We  might  continue  in  this  way  and  we  should  then  find  that  the 
smaller  the  number  of  phases  with  an  equal  number  of  components  the 
greater  the  variance.  Thus  if  "  phase  "  be  denoted  by  P,  "  component  " 
by  C,  and  "  variance  "  or  "  degrees  of  freedom  "  by  F,  then 

when          C-P  =  1,  F  =  3 

C-P=0,  F=2 

C-P=-1,  F=l 

C-P=-2,  F=Q 

If  we  examine  these  values  we  find  that  in  every  case  F  =  C—  P-f-2. 
This  is  a  general  relationship,  holding  in  all  cases,  and  is  known  as  the 
"  Phase  Rule." 

Applications  of  the  Phase  Rule. — In  using  the  phase  rule  for  the 
solution  of  chemical  problems  it  is  customary  to  fix  one  or  more  of  the 
independent  variables  and  then  attempt  to  change  the  others,  noting 
in  the  meantime  what  happens.  The  data  thus  obtained  are  usually 
|  plotted  as  a  curve,  and  from  the  shape  of  the  curve  it  is  possible  to  tell 
what  the  variance  of  the  system  is.  Knowing  the  variance  and  other 
factors,  such  as  the  number  of  components,  we  can  work  out  the  struc- 
ture of  the  system.  A  few  examples  will  help  to  make  the  procedure 
clear : 


240  HETEROGENEOUS  EQUILIBRIUM 

(1)  Does  potassium  nitrate  exist  in  two  forms,  and,  if  so,  where  does  one  form 
change  into  the  other? 

This  is  a  system  of  one  component,  KNOs,  and  at  the  point  of  change 
from  one  phase  to  the  other  there  should  be  two  phases.  Therefore 
F=  1  —  2+2,  or  1 :  in  other  words,  the  system  is  uni variant.  It  is  exactly 
like  the  system  water-ice,  and  will  give  the  same  sort  of  curve  if  treated  in 
the  same  way.  Suppose  we  take  some  water  at  ordinary  temperature,  fix 
the  pressure  at  one  atmosphere,  and  then  slowly  cool  it,  noting  the  fall 
in  temperature  per  minute.  If  we  plot  the  temperatures  as  ordinates 
and  time  as  abscissae  we  shall  obtain  a  curve  like  the  following: 


Time 
FIG.  31. — A  Time-Temperature  Curve. 

The  water  alone  represents  a  divariant  system,  as  mentioned  above; 
and,  although  the  pressure  has  been  fixed,  the  temperature  may  change 
also  without  destruction  of  phase.  This  is  shown  by  the  curve  A B, 
which  falls  evenly  with  the  time. 

When  the  temperature  reaches  0°  a  second  phase,  ice,  begins  to 
separate.  We  now  have  two  phases  and  one  component,  and  the 
system  is  univariant.  But  we  have  already  fixed  one  variable  (the 
pressure);  therefore  during  the  change  from  one  phase  to  the  other, 
when  two  phases  are  present,  the  temperature  cannot  change.  This  is 
indicated  by  the  line  BC  which  runs  parallel  to  the  axis. 

After  the  change  of  phase  is  over,  we  have  only  one  phase  (ice); 
and  with  one  phase  and  one  component  the  system  again  becomes 
divariant  as  at  first. 

To  return  now  to  the  case  of  potassium  nitrate : 

If  we  heat  potassium  nitrate  nearly  to  its  melting-point  and  then 
allow  it  to  cool  slowly  we  obtain  a  cooling  curve  exactly  like  the  one 
above.  At  first  we  have  one  phase  only  and  one  component,  and  the 
system  is  divariant.  At  129°  a  second  phase  appears  and  the  system 
becomes  univariant.  But  with  pressure  fixed  there  are  no  degrees  of 
freedom,  so  a  break  in  the  curve  appears  as  at  BC.  Later  the  curve 
falls  evenly,  indicating  a  divariant  system  of  one  phase. 


APPLICATIONS  OF  THE  PHASE  RULE  241 

The  results  here  obtained  are  typical:  In  any  case  where  a  transition 
from  one  phase  to  another  occurs,  we  obtain  a  cooling  curve  with  a  break 
as  above. 

(2)  Does  hydrogen  form  a  compound,  or  a  solution,  with  palladium? 

This  system  contains  two  components,  hydrogen  and  palladium. 
If  a  compound  is  formed  we  shall  have  three  phases — gas,  compound,  and 
palladium.  With  three  phases  and  two  components  the  system  should 
be  univariant.  If  a  solution  is  formed  we  shall  have  two  phases- — gas 
and  solution.  With  two  phases  and  two  components  the  system  should 
be  divariant. 

The  univariant  system — gas,  compound,  and  palladium — should  be 
exactly  like  a  salt  hydrate  system  containing  vapor,  hydrate,  and  anhy- 
drous salt,  and  should  give  the  same  kind  of  pressure-volume  curve. 
If,  for  example,  we  place  some  anhydrous  copper  sulphate  in  a  tube  over 
mercury,  having  above  it  water  vapor  under  a  pressure  of  2  mm.,  we 
may  decrease  the  volume  of  the  vapor  by  raising  the  mercury  and  thus 
raise  the  pressure.  If  we  do  this  we  shall  obtain  a  curve  like  AB  in 
the  diagram  below. 


Volume 
FIG.  32. — A  Pressure- Volume  Curve. 

It  is  simply  a  Boyle's-law  curve.  We  have  two  components  and 
two  phases  present,  and  so  the  system  is  divariant.  Temperature  is 
fixed,  but  pressure  may  still  be  varied  as  shown. 

When  the  pressure  reaches  4.4  mm.  the  monohydrate  begins  to  be 
formed.  The  system  then  has  three  phases,  as  noted  above,  and  so  is 
univariant.  With  temperature  fixed,  therefore,  no  freedom  remains 
and  so  the  pressure  remains  constant,  as  seen  in  BC.  After  the  salt  is 
all  changed  to  monohydrate  the  system  returns  to  two  phases,  and  is 
again  divariant. 

This  is  exactly  the  kind  of  curve  obtained  in  the  liquefaction  of  a  gas, 
and  for  the  same  reason. 

The  application  in  the  case  of  hydrogen  and  palladium  is  obvious. 
If  the  compound  is  formed  the  curve  will  be  like  the  one  above. 


242 


HETEROGENEOUS  EQUILIBRIUM 


If  not,  it  will  be  a  divariant  curve  (A  B  or  CD)  all  the  way.  It  proves 
to  be  the  latter;  therefore,  no  compound  is  formed. 

(3)  Eutectic  alloys  and  the  phase  rule. 

When  a  melted  metal  is  allowed  to  cool  slowly,  we  obtain  the  same 
kind  of  a  time-temperature  curve  as  with  water;  that  is,  the  curve 
shows  first  the  gradual  fall  and  then  the  single  horizontal  break.  If, 
however,  we  have  two  metals  mixed  together  which  are  completely 
miscible  when  melted,  and  only  slightly  soluble  in  each  other  when  solid, 
we  note  a  quite  different  behavior.  Take,  for  example,  tin  and  lead. 
If  a  mixture  of,  say  70  per  cent  lead  and  30  per  cent  tin,  is  melted,  the 
two  metals  mix  perfectly  with  each  other.  If  the  mixture  is  allowed 
to  cool  slowly,  and  a  time-temperature  curve  drawn,  the  usual  fall  is 


500°-- 


400- - 


100-  - 


*  Pb.  1 


0      90        80        70        60        50        40        30        20        10 


0         10        20        30        40        50        60        70        80        90       IQOjfBfc. 
FIG.  33. — Cooling  Curves  for  Alloys  of  Tin  and  Lead. 

noted  down  to  about  260°.  At  this  temperature  the  lead  begins  to 
solidify  just  as  water  freezes.  The  appearance  of  the  solid  phase  lowers 
the  variance  of  the  system  and  thus  produces  a  break  in  the  curve. 
But  we  have  here  a  solution  of  tin  in  lead;  and,  just  as  in  the  case  of  a 
water  solution,  the  freezing-point  of  the  lead  is  lowered.  The  separation 
of  some  solid  lead  increases  the  concentration  of  the  solution,  and  so 
further  lowers  the  freezing-point.  We  have  thus  an  infinite  number  of 
freezing-points,  one  coming  after  the  other;  and  the  result  is  a  gradual 
fall  in  the  curve  at  a  different  rate  than  that  for  the  pure  metal.  The 
effect  is  usually  designated  as  a  "  hold."  This  is  seen  at  A  in  curve  1 
Fig.  33. 

When,  due  to  the  freezing  out  of  the  lead,  the  solution  becomes 
saturated  with  tin,  both  metals  separate  together    in  fine  crystals. 


APPLICATIONS  OF  THE  PHASE  RULE 


243 


At  this  point  we  have  a  system  of  two  components  (Pb  and  Sn)  and  four 
phases  (Sn,  Pb,  solution,  vapor)  which,  according  to  the  phase  rule, 
should  be  non- variant.  We  therefore  have  a  complete  hold  in  the  curve, 
as  seen  at  B,  which  continues  until  the  whole  mass  has  solidified.  The 
mixture  of  fine  crystals  separating  together  is  called  a  "  eutectic";  and 
the  temperature  at  which  the  separation  occurs  is  called  the  "  eutectic 
point. "  At  the  eutectic  point  we  have  a  saturated  solution  of  each 
metal  in  the  other;  hence  the  lowest-melting  alloy  that  can  be  made  of 
these  two  metals. 

Note  now  that  no  matter  what  relative  proportions  of  the  two  metals 
we  start  with,  the  second  hold  in  the  curve  always  comes  at  the  same 
temperature  (180°).  If  we  happen  to  start  with  the  proportions  called 
for  by  the  eutectic  mixture  (37  per  cent  lead  and  63  per  cent  tin)  there 
will  be  no  separation  of  either  metal  until  the  eutectic  point  is  reached, 
and  only  one  hold  in  the  curve  will  be  noted  (see  curve  4) .  To  find  what 
the  eutectic  mixture  is,  however,  it  is  not  necessary  to  use  this  mixture 
itself.  If  we  make  up  about  four  mixtures,  two  rich  in  tin  and  two  rich 
in  lead,  and  obtain  their  curves,  we  can  find  the  eutectic  mixture  with 


Sn 


FIG.  34. — Cooling  Curve  showing  a  Maximum. 

fair  accuracy  by  connecting  the  points  where  the  first  holds  begin,  and 
extending  the  lines  thus  formed  until  they  meet.  (The  dotted  lines  OC 
and  DC  in  the  diagram.) 

It  is  interesting  to  note  that  tin  solder  is  the  eutectic  mixture  of  tin 
and  lead.  Plumber's  solder,  used  in  "  wiping  "  joints,  contains  about 
67  per  cent  lead.  What  is  desired  in  the  latter  case  is,  of  course,  an 
alloy  which  will  deposit  crystals  of  one  component  first,  giving  a  mushy 
mass  which  can  be  worked  into  shape,  and  finally  becoming  solid  some- 
what later. 

In  some  cases  metals  unite  to  form  compounds.  When  this  happens 
the  curves  formed  by  connecting  the  first  hold  points  usually  show  a  maxi- 
mum. The  curve  of  Fig.  34  for  mixtures  of  magnesium  and  tin  shows 
this.  The  effect  here  seen  is  due  to  the  fact  that  the  compound  is  a  phase 


244  HETEROGENEOUS  EQUILIBRIUM 

in  which  either  of  the  metals  is  soluble.  The  addition  of  either 
metal  to  the  mixture  represented  by  the  maximum  therefore  lowers  the 
freezing-point  to  a  eutectic.  (E\  and  E%.)  We  must  not  stop  for  dis- 
cussion of  this  matter  here.  We  can  only  refer  to  books  on  metallog- 
raphy for  fuller  treatment.* 

EXERCISES. 

1.  What  is  meant  by  heterogeneous  equilibrium? 

2.  Develop  the  equation  (A^/(AZ]  =  K  for  a  physical  equilibrium. 

3.  Discuss  the  law  of  "  partition  "  as  a  case  of  physical  equilibrium.     Describe 
the  cases  of  succinic  acid  in  ether  and  water,  and  bromine  in  water  and  carbon 
tetrachloride. 

4.  Discuss  the  theory  of  "  extraction,"  and  the  common  test  for  the  halogens. 
6.  What  is  a  hydrate?     Prove  that  a  hydrate  is  a  compound  with  water. 

6.  What  governs  the  gain  or  loss  of  water  by  a  hydrate?     Example?     What  is 
"  efflorescence"? 

7.  Discuss  the  equilibrium  between  the  several  hydrates  of  copper  sulphate  and 
the  atmospheric  moisture. 

8.  Discuss  the  principle  of  desiccation  by  means  of  anhydrous  salts  or  hydrates. 
What  precautions  are  necessary  to  make  the  action  most  effective? 

9.  How  does  adsorption  enter  into  the  matter  of  desiccation  by  means  of  salts 
and  other  substances? 

10.  Draw  a  diagram  representing  the  equilibrium  curves  for  water,  ice,  and  water 
vapor,  and  discuss  all  the  equilibrium  conditions  there  shown. 

11.  What  is  the  relation  between  the  "  triple  point  "  and  the  freezing-point  of 
water? 

12.  Who  developed  the  phase  rule,  and  when?     Why  was  it  not  used  at  first? 
How  was  it  made  available  for  general  use,  and  by  whom? 

13.  What  are  the  general  postulates  of  the  phase  rule? 

14.  Define  phase,  component,  degrees  of  freedom.     Examples? 

16.  Present  examples  showing  how  the  variance  of  a  system  is  related  to  the 
number  of  phases  and  components. 

'  16.  State  the  phase  rule  in  terms  of  the  symbols  C,  P,  and  F. 

17.  How,  in  general,  is  the  phase  rule  applied  to  the  working  of  chemical  problems? 

18.  Show  exactly  how  the  phase  rule  answers  the  question:    "  Does  potassium 
nitrate  exist  in  two  forms,  and  just  where  does  one  form  change  into  the  other?" 

19.  How  does  the  phase  rule  answer  the  question,   "  Does  hydrogen  form  a  com- 
pound, or  a  solution,  with  palladium"? 

20.  In  the  light  of  the  phase  rule,  what  sort  of  curve  should  be  obtained  by  plotting 
time-temperature  of  a  melted  alloy? 

21.  What  is  a  eutectic  alloy?     How  may  the  composition  be  determined? 

22.  How  do  "  tin  solder  "  and  "  plumber's  solder  "  act  when  cooling?     Explain. 

23.  What  sort  of  curve  is  obtained  by  plotting  first  hold  points  for  an  alloy  in 
which  two  metals  are  combined? 

24.  Show,  by  application  of  the  phase  rule,  why  a  salt  hydrate  does  not  give  a 
definite  vapor  pressure  at  a  fixed  temperature  unless  mixed  with  a  lower  hydrate  or 
the  anhydrous  salt. 

*  See,  for  example,  Principles  of  Metallography,  by  R.  S.  Williams. 


CHAPTER  XVIII 
COMPLEX  EQUILIBRIUM 

WE  have  studied  homogeneous  equilibrium  and  heterogeneous 
equilibrium,  and  we  must  now  take  up  matters  involving  both  kinds  of 
equilibrium  simultaneously.  For  want  of  a  better  term,  we  shall  call 
this  "  complex  equilibrium." 

The  Solubility  Product  Principle. — The  double,  or  complex,  equi- 
librium mentioned  above  was  first  noted  and  developed  by  Nernst* 
in  1889.  It  involves  the  two  kinds  of  equilibrium  as  mentioned,  but  on 
the  heterogeneous  side  it  involves  mainly  only  different  phases  of  the 
same  substance — what  we  have  called  "  physical  equilibrium."  In  our 
development  of  the  law  we  may,  therefore,  confine  our  discussion  to  this. 
We  will  proceed  by  use  of  an  example,  namely,  the  case  of  silver  acetate: 

When  silver  acetate  is  brought  in  contact  with  water  it  dissolves 
until  at  16°  C.  its  molar  concentration  is  0.0603  (about  M/16).  What- 
ever is  added  after  this  remains  over  in  the  solid  phase.  The  part  in 
solution  is  ionized  to  the  extent  of  about  71  per  cent,  the  ions  and  non- 
ionized  molecules  being  in  equilibrium  as  indicated  by  the  equation 

Ag  acf  ^  Ag++ac~ 

But  the  solid  is  in  physical  equilibrium  with  the  non-ionized  mole- 
cules, and  this  may  be  indicated  thus: 

Ag  ac  (solid)  *=»  Ag  ac  (dissolved) 

Altogether,  then,  we  have  two  simultaneous  equilibria,  thus: 
Ag  ac  (solid)  ±=>  Ag  ac  (dissolved)  ±=>  Ag++ac~ 

This  is  the  condition  where  we  have  a  saturated  solution  of  pure 
silver  acetate  in  contact  with  the  undissolved  solid.  The  solid  is  in 
equilibrium  with  the  non-ionized  molecules,  the  molecules  are  in  equi- 
librium with  the  ions. 

*  Zeitschr.  physikal.  Chemie,  4,  372. 

t  "  ac  "  here  stands  for  the  acetate  radical,  C2H3O2~;  we  use  it  simply  for  con- 
venience. 

245 


246  COMPLEX  EQUILIBRIUM 

To  make  the  discussion  more  general,  let  us  suppose  that  the  ion 
concentrations  are  either  equal  or  unequal;  that  is,  suppose  we  have 
either  the  condition  represented  above  or  a  case  where  the  concen- 
tration of  one  ion  has  been  lowered  by  the  common  ion  effect  or  other- 
wise. What,  then,  will  follow? 

According  to  the  law  of  physical  equilibrium,  the  ratio  between 
the  concentration  of  the  solid  phase  and  that  of  the  dissolved  molecules 
is  a  constant,  thus 

Ag  ac  (solid)      _  ^ 
Ag  ac  (dissolved) 

Now  the  concentration  of  the  solid  is,  of  course,  fixed  *  for  any  given 
temperature;  and  since  the  ratio  between  the  concentrations  of  the  solid 
and  the  dissolved  phases  is  a  constant,  it  follows  that  the  concentration 
of  the  dissolved  phase  (the  non-ionized  molecules)  is  also  a  constant. 
Note  that  this  is  independent  of  the  concentrations  of  the  ions,  which 
may  have  any  possible  values  within  wide  limits. 

Now,  according  to  the  law  of  chemical  equilibrium,  the  ratio  between 
the  ion  product  and  the  concentration  of  the  non-ionized  molecules  is 
also  a  constant. 


(Ag  ac) 

Here  also  the  value  of  the  ratio  is  independent  of  the  concentrations  of 
the  ions.  We  note,  furthermore,  that  the  concentration  of  the  non- 
ionized  molecules  appearing  here  is  the  factor  which  we  have  just  shown 
above  to  be  a  constant.  We  thus  see  that  the  ion  product,  giving  a 
constant  ratio  with  this,  must  also  be  a  constant. 

Note  now  exactly  what  we  have  shown:  In  a  saturated  solution  of 
silver  acetate,  where  trie  ion  concentrations  may  or  may  not  be  equal, 
both  the  ion  product  and  the  concentration  of  the  non-ionized  molecules 
are  constants,  f 

We  may  now  extend  the  statement  by  saying  that  what  is  true  of 
silver  acetate  is  true  also  of  other  substances:  both  the  ion  product  and 
the  concentration  of  the  non-ionized  molecules  in  a  saturated  solution  are 
constants.  This  is  the  ion-product  principle  as  first  developed  by 
Nernst.  We  shall  note  some  modifications  as  we  proceed. 

The  ion  product  in  a  saturated  solution  is  usually  spoken  of  as  the 
"  solubility  product  "  because  it  functions  as  a  measure  of  solubility. 

For  compounds  like  lead  chloride,  which  ionize  so  as  to  produce  more 
than  one  ion  of  a  kind,  the  solubility  product  contains  the  power  of  the 

*  The  concentration  of  a  solid  is  proportional  to  its  density. 
t  We  assume  a  constant  temperature,  of  course. 


CALCULATION  OF  THE  SOLUBILITY  PRODUCT          247 

ion  concentration  just  as  does  the  mathematical  equation  for  the  equi- 
librium constant.  Thus,  the  solubility  product  for  lead  chloride  contains 
the  factors  (Pb++)  and  (Cl~)2.  This  should  cause  no  surprise  and 
should  need  no  discussion. 

Calculation  of  the  Solubility  Product. — The  calculation  of  the  solu- 
bility product  in  any  case  consists  simply  in  determining  the  values 
for  the  ion  concentrations  in  the  saturated  solution  and  then  multiplying 
them  together,  not  forgetting,  of  course,  to  use  the  power  of  a  concen- 
tration where  called  for. 

The  solubility  product  for  silver  acetate  is  calculated  as  follows: 
We  have  noted  that  the  saturated  solution  at  16°  is  0.0603  molar. 
Conductivity  measurements  show  that  the  salt  in  this  solution  is  ionized 
to  the  extent  of  71  per  cent.  This  means  that  the  concentration  of  the 
ionized  part  is  0.71X0.603,  or  0.0428  mole  per  liter.  Now,  each  mole 
which  ionizes  produces  one  mole  of  silver  ion,  Ag+,  and  1  mole  of  acetate 
ion,  ac~.  Therefore  the  0.0428  mole  produces  0.0428  mole  of  Ag+  and 
0.0428  mole  of  ac.~~  These  make  up  the  concentrations  (Ag+)  and  (ac~). 
the  factors  in  the  solubility  product.  The  solubility  product  itself  is, 
therefore,  0.0428X0.0428,  or  0.00183. 

The  solubility  product  for  lead  chloride  is  calculated  in  nearly  the 
same  way,  but  involves  the  squaring  of  the  chloride-ion  concentration. 
The  solubility  of  this  salt  in  pure  water  at  20°  is  given  as  19.46  gm.  per 
liter.  The  molar  weight  of  lead  chloride  is  278.  The  solubility,  there- 
fore, amounts  to  19.46/278,  or  0.07  mole  per  liter.  At  this  dilution  the 
salt  is  80  per  cent  ionized.  The  concentration  of  the  ionized  part  is, 
therefore,  0.07X0.80,  or  0.056  mole.  Each  mole  of  PbCl2  which  ionizes 
produces  1  mole  of  Pb++  and  2  moles  of  Cl~.  This  gives,  for  the  con- 
centration of  the  Pb++  ion,  the  value  0.056,  and  for  the  concentration 
of  the  Cl-  0.056X2,  or  0.112.  Since  the  solubility  product  for  lead 
chloride  involves  (Pb++)X(Cl-)2,  its  value  is  0.056  X(0.11gg,  or 
0.000702. 

Effect  of  Foreign  Salts  on  the  Solubility  Product. — We  have  noted 
in  earlier  sections  that  the  ionization  of  electrolytes  is,  in  general, 
apparently  increased  by  the  presence  of  foreign  salts  (salt  effect)  and 
that  solubility  is,  in  general,  decreased  *  by  the  presence  of  foreign  salts. 
Applying  these  two  factors  to  the  solubility-product  principle,  we  note 
an  effect  in  opposite  directions.  Lowering  the  molecular  concentration 
without  changing  the  degree  of  ionization  would  lower  the  ion  product. 
But  the  salt  effect  tends  to  increase  the  degree  of  ionization,  and  this  in 
turn  raises  the  ion  product.  In  cases  so  far  studied,  it  seems  that  for 

j  *  There  are  exceptions  to  this  rule.  For  example,  the  solubility  of  Ca(OH)2  is 
increased  by  the  presence  of  KC1. 


248  COMPLEX  EQUILIBRIUM 

concentrations  not  greater  than  0.5  these  two  tendencies  counter- 
balance.* The  net  result,  then,  of  the  presence  of  foreign  salts  seems 
to  be  to  lower  the  molecular  solubility  but  to  leave  the  ion  product  a 
constant.  The  application  of  this  will  be  seen  as  we  proceed. 

Theory  of  Precipitation. — If  we  mix  a  certain  volume  of  M/10  silver 
nitrate  solution  with  an  equal  volume  of  M/10  sodium  acetate  solution, 
no  precipitate  is  formed.  If  we  use  M/5  solutions  in  each  case  we  obtain 
a  rather  abundant  precipitate  of  silver  acetate.  Let  us  find  the  reason 
for  this  difference. 

When  the  two  M/10  solutions  are  mixed,  each  is  diluted  by  the 
other,  so  that  their  concentrations  become  only  M/20,  or  0.05.  M/20 
silver  nitrate  is  about  85  per  cent  ionized.  The  silver  ion  concentration 
is  therefore  0.85X0.05,  or  0.0425.  M/20  sodium  acetate  is  83  per  cent 
ionized,  and  therefore  gives  a  concentration  of  acetate  ion  of  0.83X0.05, 
or  0.0415.  The  product  of  the  concentrations  of  the  silver  ion  and  the 
acetate  ion  is  0.0425X0.0415,  or  0.00176.  Now  we  have  seen  above 
that  the  ion  product  for  silver  acetate  in  a  saturated  solution  (the  solu- 
bility product)  is  0.00183.  The  ion  product  here  available  is  less  than 
this,  and  therefore  represents  a  solution  which  is  not  saturated,  not  to 
speak  of  furnishing  an  excess  (a  precipitate).  This  shows  plainly  why 
no  precipitate  was  formed  when  the  M/10  solutions  were  mixed. 

When  M/5  solutions  are  mixed  they  become  M/10.  M/10  silver 
nitrate  is  81  per  cent  ionized,  and  therefore  yields  a  silver  ion  concen- 
tration of  0.81X0.1,  or  0.081.  M/10  sodium  acetate  is  79  per  cent 
ionized,  and  therefore  yields  an  acetate  ion  concentration  of  0.79X0.1, 
or  0.079.  The  ion  product,  (Ag+)X(ac~),  is  0.081X0.079,  or  0.0064, 
and  this  is  far  in  excess  of  the  ion  product  in  a  saturated  solution  of  silver 
acetate.  The  two  ions  therefore  unite  to  form  non-ionized  silver  acetate, 
until  the  ion  product  falls  to  the  value  allowed  in  a  saturated  solution, 
namely  0.00183.  But  whether  a  precipitate  forms  or  not  involves  more 
than  this :  It  depends  on  whether  enough  of  the  non-ionized  part  can  be 
formed  to  more  than  saturate  the  solution,  and  still  leave  the  ion  product 
equal  to  the  solubility  product.  This  we  can  calculate  as  follows: 

If  x  is  the  largest  concentration  of  molecules  that  can  be  formed  and 
still  leave  the  ion  product  equal  to  the  solubility  product,  the  relation 
indicated  by  the  following  equation  must  hold: 

[(Ag+)  -  x]  X  [(ac~)  -x]=  0.00183 

*  Stieglitz,  Jour.  Am.  Chem.  Soc.,  30,  946,  (1908).  For  quantitative  results  see 
Stieglitz,  Qual.  Anal.,  Vol.  I,  pp.  146,  147.  For  contrary  views  see  Hill,  Jour.  Am. 
Chem.  Soc.,  32,  1186  (1910)  and  papers  by  Harkins,  ibid.,  1911. 


SOLUTION  OF  PRECIPITATES  249 

Substituting  the  ion  concentrations  coming,  as  shown  above,  from 
the  silver  nitrate  and  the  sodium  acetate,  we  have  the  following: 

(0.081  -x)X  (0.079  -x)  =0.00183 

Solving,  we  find  x  to  be  0.038.  This  is  the  concentration  of  non-ionized 
molecules  that  can  be  formed  and  leave  the  ion  concentration  equal  to 
the  solubility  product.  Now,  we  have  shown  that  a  saturated  solution 
of  silver  acetate  is  0.0603  molar,  and  that  the  salt  in  this  solution  is 
71  per  cent  ionized.  This  leaves  29  per  cent  for  the  non-ionized  part, 
and  29  per  cent  of  0.0603  is  0.0175.  This  is  the  highest  concentration 
of  non-ionized  molecules  which  can  exist.  The  concentration  formed 
above  by  union  of  Ag+  and  ac~  is  much  larger  than  this.  The  excess, 
therefore,  must  come  down  as  a  precipitate. 

What  we  have  shown  here  in  detail  to  occur  with  a  mixture  of  silver 
nitrate  and  sodium  acetate  occurs  also  in  other  cases.  We  may  now, 
therefore,  make  a  general  statement  concerning  the  matter,  which  we 
may  call  the  "  rule  for  precipitation" :  Whenever  two  ions  are  brought 
together  in  such  concentration  that  they  can  form  more  than  the  saturation 
amount  of  the  non-ionized  substance  and  still  leave  the  ion  product  equal 
to  the  solubility  product,  precipitation  will  occur. 

We  should  probably  note  before  leaving  this  subject  that  in  many 
cases  the  compound  precipitated  is  so  insoluble  that  the  part  remaining 
in  solution  may  be  regarded  as  completely  ionized.  This  means  that 
the  concentration  of  the  non-ionized  molecules  is  practically  zero.  In 
calculating,  then,  whether  precipitation  will  occur  in  such  cases,  it  is 
only  necessary  to  determine  whether  the  ion  product  exceeds  the  solu- 
bility product.  It  is  evident  that  this  fact  makes  the  calculation  very 
much  simpler  than  that  necessary  in  the  above  case.  This  will,  no 
doubt,  be  a  comforting  assurance. 

Solution  of  Precipitates. — In  the  light  of  what  we  have  said  above 
about  precipitation,  the  discussion  of  this  topic,  which  is  the  exact 
converse,  may  be  made  very  brief.  The  general  rule  for  solution  of 
precipitates  is  as  follows:  Whenever  a  solid  is  in  contact  with  a  solution 
containing  its  ions  in  smaller  concentration  than  is  necessary  to  make  the 
ion  product  equal  the  solubility  product  the  solid  will  dissolve.  In  practice 
this  usually  amounts  to  saying  that,  if  a  solid  is  in  contact  with  its  sat- 
urated solution  and  the  ion  product  can  in  some  way  be  lowered,  the  solid 
will  dissolve. 

To  use  our  stock  example,  suppose  we  place  solid  silver  acetate  in 
contact  with  the  solution  formed  by  mixing  equal  volumes  of  M/10 
silver  nitrate  and  sodium  acetate.  The  ion  product  is  here  lower  than 
the  solubility  product,  as  we  have  shown.  In  such  a  solution  silver 


250  COMPLEX  EQUILIBRIUM 

acetate  will  dissolve.  This,  of  course,  is  a  very  simple  case:  we  begin 
with  an  unsaturated  solution.  Suppose,  on  the  other  hand,  we  have 
silver  acetate  in  contact  with  its  saturated  solution;  how  can  we  cause 
it  to  dissolve?  The  simplest  way  to  bring  about  this  result  is  to  add 
some  ion  which  can  unite  with  one  of  the  ions  present  to  form  a  non- 
ionized  or  slightly  ionized  substance.  Thus  we  may  add  hydrogen 
ion  in  the  form  of  nitric  acid.  If  we  do  this  we  shall  have  the  following 
equilibria  : 

I 
Ag  ac  (solid)  ±=>  Ag  ac  (dissolved)  +±  Ag+-|-ac~ 

HNO3<=±NO3~+H+ 

4T 

Hac 

From  our  discussion  of  ionic  equilibrium,  we  note  at  once  that  non- 
ionized  acetic  acid  will  be  formed,  and  we  know  that  if  the  concentration 
of  the  hydrogen  ion  is  made  large  enough  the  concentration  of  the  acetate 
ion  may,  by  this  process,  be  reduced  almost  to  the  vanishing  point. 
This  will,  of  course,  reduce  the  ion  product,  (Ag)X(ac~),  far  below  the 
solubility  product  for  silver  acetate;  more  Ag  ac  will  ionize,  thus  lower- 
ing its  concentration,  and  this  will  disturb  the  physical  equilibrium, 
resulting  in  solution  of  the  solid. 

The  above  is  a  typical  method  of  causing  the  solution  of  a  precipitate. 
There  are,  of  course,  other  ways  of  reducing  the  ion  concentrations,  but 
the  result  is  always  the  same :  any  method  which  reduces  the  ion  product 
below  the  solubility  product  value  will  cause  solution.  Note  that  in 
the  case  described  the  acid  added  (HNOs)  was  stronger  than  the  one 
produced  (H  ac).  This  must  always  be  so.  We  could  not,  for  example, 
dissolve  silver  chloride  in  acetic  acid,  for  we  could  not  thus  obtain 
sufficient  hydrogen  ion  to  cause  the  formation  of  any  appreciable 
amount  of  non-ionized  HCL  It  is  a  general  rule  that  so-called  "  insol- 
uble "  salts  of  weak  acids  dissolve  in  stronger  acids  because  of  the  forma- 
tion of  the  weak  acid  and  consequent  reduction  of  the  ion  product.  To 
determine  beforehand  whether  such  solution  should  occur  one  need 
only  look  up  the  ionization  constants  for  the  acids  concerned.*  We 
may  thus  answer  the  question:  will  calcium  oxalate  dissolve  in  acetic 
acid?  That  solution  may  occur  here  it  will  not  be  necessary  that  the 
complete  acid,  H2C2O4,  be  formed;  it  will  be  quite  sufficient  if  the  bin- 
oxalate  ion,  HC2C>4~,  be  formed.  But  when  we  look  up  the  data  we 

*  It  is  also  necessary  that  the  salt  be  at  least  slightly  soluble  in  water,  so  as  to 
give  an  appreciable  concentration  of  its  ions,  and  unless  the  attacking  acid  is  consid- 
erably the  stronger  solution  will  be  very  slow. 


PRECIPITATION  BY   MEANS  OF  WEAK  ACIDS  251 

find  that  the  constant  for  this  ion  (the  secondary  ionization  of  H2C204) 
is  5X10~5,  which  is  larger  than  the  constant  for  acetic  acid.  The  bin- 
oxalate  ion  is  therefore  a  stronger  acid  than  acetic;  and  from  this, 
we  conclude  that  calcium  oxalate  need  not  be  expected  to  dissolve  in 
acetic  acid.  In  practice  it  does  not. 

Precipitation  by  Means  of  Weak  Acids  and  their  Salts :  Solution  of 
the  Precipitates. — (a)  Carbonic  Acid  and  Carbonates. — A  solution  of 
carbon  dioxide  (carbonic  acid)  does  not  cause  precipitation  of  calcium 
carbonate  when  added  to  a  solution  of  calcium  chloride  or  nitrate.  If, 
however,  we  afterwards  add  ammonium  hydroxide  to  the  same  mixture, 
we  obtain  a  precipitate  at  once.  In  the  light  of  our  discussion  above,  the 
explanation  for  this  difference  is  simple.  Carbonic  acid  is  so  weak  that 
the  ion  product,  (Ca++)  X  (CO3=),  is  less  than  the  solubility  product  for 
CaCOa,  even  when  the  concentration  of  the  calcium  ion  is  large.  This 
can  be  seen  from  the  following  data : 

A  saturated  solution  of  CO2,  as  ordinarily  prepared  (not  taking  into 
account  the  pressure  of  the  gas  above  the  solution)  is  perhaps  of  M/100 
concentration.  The  secondary  ionization  of  this  gives  rise  to  a  car- 
bonate ion  concentration  of  about  7X10"11.*  A  saturated  solution  of 
calcium  chloride  is  5.4  molar.  If  we  assume  that  this  is  30  per  cent 
ionized  it  will  give  a  calcium  ion  concentration  of  5.4X0.30,  or  1.62. 
The  maximum  ion  product  obtainable,  -then,  with  carbonic  acid  and 
calcium  chloride  is  ^ 

1.62X7X10-11,  or  1.13X16-10 

Now  a  saturated  solution  of  CaCOs  is  0.000,13  molar.  If  we  assume 
that  at  this  great  dilution  the  salt  is  completely  ionized,  the  concen- 
tration of  each  of  the  ions,  Ca++  and  CO3=  will  be  the  same  as  this,  and 
the  solubility  product  will  be  (0.00013)2,  or  1.7X1Q-8.  Since  this  is 
more  than  one  hundred  times  as  great  as  the  maximum  ion  product 
obtainable  with  calcium  chloride  and  carbonic  acid,  the  reason  why  no 
precipitate  is  formed  is  quite  obvious. 

When  ammonia  or  sodium  hydroxide  is  added  to  the  above  mixture, 
we  obtain  the  highly  ionized  salt,  ammonium  or  sodium  carbonate. 
The  concentration  of  the  COs=  ion  from  this  is  hundreds  of  times 
greater  than  from  the  corresponding  amount  of  carbonic  acid.  The 
ion  product,  (Ca++)X(CO3=),  therefore,  immediately  exceeds  the  sol- 
ubility product  for  CaCOs,  and  precipitation  results. 

It  must  not  be  understood  from  the  above  that  carbonic  acid  will 
never  be  able  to  cause  precipitation.  It  will  give  precipitates  in  all 

*  This  is  the  same  numerically  as  the  secondary  ionization  constant.  See  topic, 
"  Ion  Concentrations  from  Ionization  Constants." 


252  COMPLEX  EQUILIBRIUM 

cases  where  the  solubility  product  of  the  compound  to  be  formed  is  low 
enough  to  be  exceeded  by  the  ion  product  which  can  be  produced.  For 
example,  lead  in  sufficient  concentration  gives  a  precipitate  with  car- 
bonic acid.  The  extent  of  such  precipitation  depends  first,  on  the 
relative  insolubility  of  the  precipitate  formed,  and  second,  on  the  nature 
of  the  negative  ion  present  in  the  salt  solution  used.  Thus,  if  lead  nitrate 
is  treated  with  carbonic  acid,  only  a  trace  of  lead  carbonate  is  pre- 
cipitated. The  H+  ion  from  the  carbonic  acid  accumulates  as  the  CO3= 
is  removed,  and  this  suppresses  the  ionization  of  the  remaining  carbonic 
acid  until  the  CO3=  concentration  falls  too  low  for  the  solubility 
product  to  be  longer  exceeded.  If  we  use  lead  acetate  instead  of  lead 
nitrate  the  H+  ion  cannot  accumulate,  being  tied  up  immediately  in  the 
form  of  non-ionized  acetic  acid.  The  reaction,  therefore,  goes  much 
farther  in  this  case. 

Carbonates  dissolve  in  nearly  all  acids,  because  most  acids  are 
stronger  than  carbonic  acid  (see  Ionization  Constants) .  This  solubility 
is  also  partly  due  to  the  fact  that  the  carbonic  acid  formed  breaks  up, 
giving  the  volatile  product,  C02.  The  latter  reason  explains  the  fact 
that  carbonates  are  decomposed  by  boiling  solutions  of  boric  acid  or  by 
silicic  acid,  both  of  which  are  weaker  than  carbonic  acid.  The  slight 
amount  of  non-ionized  carbonic  acid  formed  in  the  establishment  of 
equilibrium  is  expelled  by  the  boiling,  and  the  process  then  repeats 
itself  until  complete  solution  results.  Note  that  boric  and  silicic  acids 
are  not  volatile.* 

(b)  Hydrosulphuric  Acid  and  Sulphides. — When  hydrogen  sulphide 
gas  is  dissolved  in  water  it  forms  a  weak  acid  somewhat  analogous  to 
carbonic.  It  is  much  used  in  qualitative  separations,  because  under 
properly  regulated  conditions  certain  metals  are  precipitated  by  it  as 
sulphides,  while  certain  others  are  left  in  solution.  The  principles 
involved  are  exactly  the  same  as  with  carbonic  acid,  as  the  following 
examples  will  show : 

When  hydrogen  sulphide  gas  is  passed  into  a  neutral  solution  of  zinc 
chloride  or  nitrate,  a  copious  precipitate  of  zinc  sulphide  is  produced. 
If  the  process  is  continued  until  nothing  further  happens,  and  the  solu- 
tion then  filtered,  however,  we  shall  find  on  testing  that  the  zinc  has  not 
been  completely  precipitated.  We  shall  find  also  that  the  solution  has 
become  distinctly  acid.  The  explanation  is  simple.  When  not  inter- 
fered with  by  any  common  ion,  H^S  gives  by  its  secondary  ionization  a 
concentration  of  sulphide  ion  (S=)  of  1.2X10~15.  With  a  large  con- 
centration of  zinc  ion  this  small  concentration  of  sulphide  ion  is  sufficient 
to  exceed  the  solubility  product  for  ZnS.  A  precipitate  therefore  forms. 
*  Boric  acid  is  slightly  volatile  with  steam. 


PRECIPITATION  BY  MEANS  OF  WEAK  ACIDS  253 

As  the  sulphide  ion  is  thus  removed,  the  hydrogen  ion,  also  coming  from 
the  H2S,  is  left  behind.  This  hydrogen  ion  must  always  be  in  equi- 
librium with  the  sulphide  ion,  and  assuming  that  the  concentration  of 
the  H2S  is  constant  (saturated  solution),  the  ion  product  is  practically 
a  constant.  Therefore  as  (H+)  is  increased  (S=)  decreases  in  the  same 
proportion.  t  Finally,  (S=)  becomes  so  small  that  the  ion  product 
(Zn++)X(S=)  no  longer  exceeds  the  solubility  product  for  ZnS,  and 
then  precipitation  stops. 

To  cause  precipitation  to  proceed  again,  we  have,  of  course,  only  to 
remove  the  accumulated  H+  ion.  To  do  this,  we  may  add  an  alkali, 
like  ammonium  hydroxide.  If  we  add  barely  enough  of  this  to  neu- 
tralize the  accumulated  H+  ion,  we  shall  have  a  return  to  the  original 
conditions;  that  is,  the  sulphide  ion  concentration  will  become  1. 2 X  10~15. 
If,  however,  we  add  an  excess,  we  shall  form  the  highly  ionized  salt, 
ammonium  sulphide,  and  the  sulphide  ion  concentration  may  then 
become  very  large.  Another  way  to  remove  the  accumulated  hydrogen 
ion  is  to  add  the  salt  of  a  very  weak  acid,  sodium  acetate  for  example, 
the  anion  of  which  at  once  ties  up  the  hydrogen  ion  to  form  the  non- 
ionized  acid.  By  either  of  these  methods  the  precipitation  of  the  zinc 
can  be  made  practically  complete. 

The  metals  of  the  second  qualitative  group,  (Cu,  Pb,  Hg,  Cd,  etc.) 
have  much  smaller  solubility  products  than  zinc  and  its  associates  in 
the  fourth  group.*  For  this  reason  they  are  precipitated  completely 
by  H2S,  even  in  the  presence  of  a  considerable  amount  of  acid  (H+  ion). 
One  or  two  of  these  metals  (particularly  cadmium)  have  such  high  solu- 
bility products,  however,  that  it  is  necessary  to  regulate  rather  carefully 
the  amount  of  acid  present  if  complete  precipitation  is  to  be  obtained. 
At  the  same  time  we  must  not  have  too  low  a  concentration  present, 
or  some  zinc  will  come  down  with  this  group.  The  allowable  concen- 
tion  is  about  0.3.  f  This  means  that  we  may  make  up  a  mixture  of 
N/10  solutions  of  the  metals  of  the  two  groups  and  may  add  enough 
acid  to  give  a  hydrogen  ion  concentration  of  0.2.  By  the  time  the  pre- 
cipitation of  group  2  is  complete,  we  may  have  an  accumulation'  of 
hydrogen  ion  from  the  EkS  amounting  to  something  near,  but  not  more 
than,  0.1.  This  will  make  the  total  concentration  0.3,  which  is  sufficient 
to  completely  prevent  the  precipitation  of  any  zinc  and  at  the  same 
time  allow  quantitative  precipitation  of  all  the  metals  of  group  2. 

The  solution  of  sulphides  in  acids  follows  the  general  rule,  and  there- 
fore need  not  be  discussed.  We  should  note,  however,  that  some  sul- 

*  For  the  solubility  products  of  several  sulphides  see  Knox,  Trans.  Faraday 
Society,  4,  44  (1908). 

t  Stieglitz,  Qualitative  Analysis,  Vol.  I,  p.  214. 


254  COMPLEX  EQUILIBRIUM 

phides  do  not  dissolve  even  in  concentrated  strong  acids.  Thus,  copper 
sulphide  refuses  to  dissolve  in  concentrated  HC1.  We  should  expect  it 
to  dissolve  because  it  is  the  salt  of  a  very  weak  acid,  and  the  ion  product 
should  be  lowered  by  the  formation  of  the  non-ionized  acid.  The  reason 
for  the  seeming  discrepancy  is,  however,  simple.  The  salt  is  so  insoluble 
and  its  solubility  product  so  low  that  the  S=  ion  factor  is  vanishingly 
small,  and,  no  matter  how  much  hydrogen  ion  we  present  to  it,  we 
cannot  induce  the  formation  of  H^S,  because  the  EbS  would  give  more 
sulphide  ion  than  the  copper  sulphide  does.* 

Precipitation  by  Means  of  Ammonium  Hydroxide  and  Sodium 
Hydroxide. — The  relative  precipitating  power  of  NH^OH  and  NaOH 
is  closely  analogous  to  that  of  a  weak  acid  and  its  salt,  and  the  difference 
depends  on  the  same  cause,  namely,  difference  in  ionization.  Ammo- 
nium hydroxide  is  a  weak  base,  and  is  therefore  subject  to  the  same 
effects  as  a  weak  acid.  Sodium  hydroxide  is  a  strong  base,  and  there- 
fore shows  very  little  reduction  in  its  precipitating  power  from  the  pres- 
ence of  a  common  ion  or  otherwise.  Note  the  following  examples: 

If  ammonium  hydroxide  is  added  to  a  solution  of  magnesium  sul- 
phate, partial  precipitation  occurs,  as  with  EkS  and  zinc.  As  the  OH~~ 
ion  from  the  NEUOH  is  removed,  the  NH4+  ion  accumulates.  As 
(NH4+)  grows  larger,  (OH~),  which  must  be  in  equilibrium  with  it, 
grows  smaller  and  smaller,  until  finally  the  ion  product  (Mg++)  X  (OH~)2 
no  longer  exceeds  the  solubility  product  for  Mg(OH)2,  and  precipitation 
then  stops.  If  ammonium  chloride  in  sufficient  amount  is  present  in 
the  solution,  ammonium  hydroxide  precipitates  no  magnesium  hydrox- 
ide at  all.  This  is,  of  course,  due  to  the  suppressing  effect  of  the  NH4+ 
ion  on  the  ionization  of  the  ammonium  hydroxide,  f 

The  effect  is  exactly  analogous  to  that  of  hydrochloric  acid  on  hydro- 
gen sulphide  or  acetic  acid. 

Ammonium  hydroxide  precipitates  ferric  iron  or  aluminum  com- 
pletely, even  in  the  presence  of  much  ammonium-chloride.  This  is 
due,  of  course,  to  the  extremely  small  solubility  products  of  ferric 
hydroxide  and  aluminum  hydroxide. 

Ammonium  hydroxide  does  not  precipitate  calcium  even  from  the 
most  concentrated  solutions,  because  the  solubility  product  of  calcium 
hydroxide  is  too  large.  Sodium  hydroxide  can  do  this  because  it  pro- 
duces a  high  concentration  of  OH~. 

Complex  Ions  in  Precipitation  and  Solution. — {(a)  Ammonia  Com- 

*  NiS  and  CoS  dissolve  with  extreme  slowness,  but  are  finally  quite  soluble  in 
acids.  Noyes,  Bray,  and  Spear,  Jour.  Am.  Chem.  Soc.,  30,  528. 

t  Loven,  Zeitschr.  anorg.  Chemie,  11,  404;  also  Herz  and  Muhs,  ibid.,  38,  138. 

t  For  an  extended  discussion  of  this  subject  see  Stieglitz,  Qualitative  Analysis, 
Vol.  I,  pp.  216-241. 


COMPLEX  IONS  IN  PRECIPITATION  AND  SOLUTION         255 

plexes. — When  ammonium  hydroxide  is  added  to  a  silver  solution,  a 
brown  precipitate  of  silver  oxide  is  at  first  produced,  as  occurs  with 
sodium  hydroxide.  If,  however,  an  excess  of  ammonium  hydroxide 
is  added,  the  precipitate  redissolves,  a  thing  which  does  not  happen 
when  sodium  hydroxide  is  used.  Investigation  has  shown  that  with 
ammonia  the  silver  forms  a  positive  complex  ion  (a  cation)  of  the  form 
Ag(NH3)2+  which  may  be  called  "  silver-ammonium."*  This  complex 
forms  a  strongly  basic  hydroxide,  Ag(NH3)2OH,f  and  soluble  salts  of 
the  type  AgCNHs^NOs.  It  is  due  to  the  solubility  of  these  salts  that 
the  very  insoluble  silver  chloride  dissolves  readily  in  ammonia.  The 
reaction  by  which  the  soluble  complex  is  formed  is  typical,  thus: 

(1)  2AgCl+2NH4QH  ->  Ag2O+NH4Cl+H2O 

(2)  Ag2O+2NH4Cl+2NH4OH  ->  2Ag(NH3)2Cl+3H2O 

2AgCl+4NH4OH  ->  2Ag(NH3)2Cl+4H2O 

Since  reaction  (2)  follows  immediately  after  Reaction  (1)  begins,  the 
production  of  the  oxide  is  not  seen.  Where  a  solution  of  the  nitrate  is 
used  it  may  be  seen,  as  noted  above,  if  the  ammonia  is  dilute  and  is  very 
cautiously  added. 

As  might  be  expected,  the  silver- ammonium  complex  dissociates 
slightly  into  its  constituents  as  indicated  by  the  equation 

Ag(NH3)2+^±Ag++2NH3 

This  is  a  reversible  reaction,  very  much  like  the  ionization  of  a  very 
weak  acid  or  base.  It,  therefore,  gives  a  constant  for  the  ratio 

(Ag+)X(NH3)2 
(Ag(NH3)2) 

which  we  shall  call  the  "  dissociation  constant."  J  The  value  for  this 
constant  is  6.8 X 10"8  at  25°. §  Like  other  reversible  reactions,  this  dis- 
sociation is  subject  to  common  ion  effect  and  all  other  equilibrium  rela- 
tions. Thus  a  large  excess  of  NH3  suppresses  the  dissociation  and  thus 
lowers  the  concentration  of  the  silver  ion,  while  removal  of  NH3  in  like 
manner  raises  the  concentration  of  the  silver  ion. 

*  Stieglitz,  Qual.  Anal.,  Vol.  I,  p.  217. 

t  This  is  a  stronger  base  than  Ba(OH)2.     See  Bonsdorf,  Ber.,  36,  2324. 

JAlso  called  the  "instability  constant."  See  Stieglitz,  Qual.  Anal.,  Vol.  I, 
p.  219  (1911). 

§  Bodlander,  Bull,  de  la  Soc.  Chim.  de  Paris,  (3)  13,  386;  also  Bodlander  and 
Fittig,  Zeitschr.  physikal.  Chemie,  39,  602. 


256  COMPLEX  EQUILIBRIUM 

Advantage  is  taken  of  our  ability  to  thus  regulate  the  dissociation 
o'f  the  silver-ammonium  complex  in  certain  analytical  separations. 
Thus,  if  we  take  a  solution  containing  barely  enough  ammonia  to 
redissolve  a  precipitate  of  silver  oxide,  and  add  to  it  a  soluble  chloride, 
we  get  a  precipitate  of  silver  chloride.  We  understand  this  to  be  due 
to  the  fact  that  the  complex  in  such  a  solution  gives  enough  silver  ion 
to  exceed  the  solubility  product  for  silver  chloride.  If,  however,  the 
solution  contains  a  moderate  excess  of  ammonia,  no  silver  chloride  is 
precipitated;  or,  if  a  precipitate  has  been  formed,  it  redissolves.  In 
such  a  solution,  which  barely  fails  to  allow  the  precipitation  of  silver 
chloride,  a  soluble  bromide  will  give  a  precipitate  of  silver  bromide. 
This  is,  of  course,  due  to  the  greater  insolubility  of  the  silver  bromide. 
A  rather  high  concentration  of  ammonia  will,  however,  prevent  even 
this.  Silver  iodide,  on  the  other  hand,  is  so  insoluble  that  it  is  almost 
impossible  to  obtain  a  high  enough  concentration  of  NHs  to  prevent  its 
precipitation.  These  differences  have  been  made  the  basis  for  the 
analytical  separation  of  chlorides,  bromides  and  iodides. 

Copper  forms  a  beautiful  blue  complex  cation  with  ammonia,  having 
the  formula  Cu(NH3)4++.*  This  is  always  seen  when  an  excess  of  am- 
monia is  added  to  a  copper  solution.  The  reaction  is  closely  analogous 
to  that  with  silver;  a  small  amount  of  ammonia  gives  the  green  hy- 
droxide, Cu(OH)2,  and  an  excess  then  gives  the  complex. 

This  complex  forms  salts  of  the  type  Cu(NH3)4Cl2  or  Cu(NH3)4SO4. 
The  soluble  base  Cu(NHs)4(OH)2,  may  also  be  formed  by  treating  the 
oxide  or  hydroxide  with  ammonium  hydroxide. 

The  dissociation  constant  for  the  cupric  ammonium  complex  is 
10~7,|  which  indicates  that  this  complex  is  somewhat  more  highly 
ionized  than  the  silver  complex.  Sodium  phosphate,  which  precipitates 
cupric  ion,  fails  to  give  a  precipitate  with  the  complex,  but  a  soluble 
sulphide  instantly  gives  a  precipitate  of  the  black  cupric  sulphide. 

Other  ammonia  complexes  are  those  of  zinc,  nickel,  and  particularly 
of  cobalt  (the  cobalt  ammines).  They  are  all  important,  but  we  cannot 
study  them  in  detail  here. 

(6)  Cyanide  Complexes. — The  cyanide  complexes  are  anions.  With 
some  of  these  the  reader  is  familiar,  as,  for  example,  the  ferro-  and  ferri- 
cyanides.  We  shall  therefore  mention  only  a  few  of  the  more  special 
cases. 

When  potassium  cyanide  is  added  to  a  solution  of  silver  nitrate, 
silver  cyanide,  AgCN,  is  precipitated ;  but  an  excess  of  KCN  redissolves 
this  to  form  the  soluble  argenticyanide,  KAg(CN)2,  in  which  the  silver 

*  Regarding  this  complex  see  Locke  and  Fassall,     Am.  Chem.  Jour.,  31,  268,  269. 
t  Euler,  Berichte,  36,  3403. 


COMPLEX  IONS  IN  PRECIPITATION  AND  SOLUTION          257 

functions  as  a  part  of  the  anion  Ag(CN)2~.  The  dissociation  constant 
of  this  complex  is  10~21,*  indicating  great  stability  or  very  slight  ioniza- 
tion.  A  soluble  chloride  fails  to  precipitate  silver  chloride  from  this 
solution.  On  the  other  hand,  a  soluble  sulphide  precipitates  silver 
sulphide  except  in  the  presence  of  a  large  excess  of  KCN,  exhibiting  the 
extreme  insolubility  of  the  sulphide. 

The  reaction  between  potassium  cyanide  and  cupric  ion  is  similar 
to  that  with  silver,  except  that  the  copper  is  first  reduced  to  the  cuprous 
condition  (colorless).  The  cupro-cyanide  complex  has  the  formula 
Cu(CN)3=,  the  potassium  salt,  K2Cu(CN)3,  being  formed  with  a  slight 
excess  of  KCN.  The  stability  of  this  complex  is  so  great  that  soluble 
sulphides  do  not  precipitate  copper  sulphide  from  it. 

Cadmium  also  forms  a  complex  cadmi-cyanide,  K2Cd(CN)4.  The 
stability  of  this  is  so  much  less  than  that  of  the  copper  complex  that 
sulphides  precipitate  cadmium  sulphide  even  in  the  presence  of  an 
excess  of  KCN.  This  fact  is  the  basis  of  the  common  qualitative  sep- 
aration of  copper  and  cadmium. 

(c)  Complex  Oxalates. — When  a  soluble  oxalate   (e.g.,  K2C204)   is 
added  to  a  solution  of  ferric  iron  the  solution  takes  on  a  greenish  color 
and  then  contains  the  complex  oxalate  ion,  Fe(C2O4)3^.     With  potas- 
sium oxalate  the  salt  formed  is  KsFe^C^s. 

The  equilibrium  relations  of  this  ion  are  interesting.  For  example, 
in  the  presence  of  an  excess  of  potassium  or  ammonium  oxalate  it  gives 
no  test  for  iron  with  potassium  ferrocyanide  or  thiocyanate,  but  it  does 
give  a  test  with  sodium  hydroxide.  In  explanation  of  this,  we  reason 
that  the  complex  furnishes  too  little  ferric  ion  to  give  a  test  with  the 
first  two  reagents  but  enough  to  give  a  visible  amount  of  the  extremely 
insoluble  hydroxide.  In  the  presence  of  a  small  amount  of  hydro- 
chloric acid,  the  first  two  tests  appear  instantly.  This  is  easily 
explained  when  we  remember  that  a  high  concentration  of  hydrogen 
ion  is  sure  to  unite  with  oxalate  ion  to  form  non-ionized  oxalic  acid 
and  thus  very  much  encourage  the  dissociation  of  the  complex. 

Note  also  the  effect  of  adding  ferric  salts.  The  addition  of  ferric 
chloride,  for  instance,  raises  the  concentration  of  the  ferric  ion  and  cor- 
respondingly decreases  the  concentration  of  the  oxalate  ion,  finally 
reducing  it  to  the  point  where  it  no  longer  gives  a  precipitate  of  calcium 
oxalate  with  a  calcium  salt. 

(d)  Complex    Tartrates   and   Lactates. — Organic   compounds   which 
contain  the  secondary  alcohol  group,— CHOH — ,  tend  to  form  complexes 
with  metals.     Among    these  are  certain  sugars,  alcohols,  and  notably 
the  hydroxy  acids,  such  as  tartaric  and  lactic. 

*  Bodlander,  Zeitschr.  anorg.  Chem.,  39,  222. 


258  COMPLEX  EQUILIBRIUM 

The  molecule  of  tartaric  acid  may  be  represented  as  (CHOH)2 — 
(COOH)2.  Copper  will  substitute  hydrogen  in  the  CHOH  groups, 
giving  (CHO)2 — Cu — (COOH)2.*  Of  course  there  is  a  tendency 
towards  slight  dissociation,  giving  Cu++  ion.  The  presence  of  a  strong 
alkali  (NaOH)  represses  this  tendency,  although  precipitating  no  copper 
hydroxide,  the  effect  being  seen  in  the  brightening  of  the  blue  color  due 
to  the  complex.  Fehling's  solution,  much  used  as  a  test  for  reducing 
sugars,  contains  this  tartrate  complex  of  copper. 

Lactic  acid  is  represented  by  the  formula  CH3 — CHOH — COOH. 
This  acid  also  forms  complexes  with  metals.  An  important  example 
is  the  complex  formed  with  ferric  iron.  This  may  be  indicated  by  the 
formula  (CH3CHO)3-  Fe— (COOH)3.  An  excess  of  sodium  hydroxide 
precipitates  iron  from  this  complex,  but  ammonium  hydroxide  does  not; 
and,  when  we  remember  that  in  analytical  work  iron  is  precipitated 
quantitatively  with  the  latter  reagent,  we  understand  something  of  the 
stability  of  the  complex. 

Equilibrium  Relations  of  Amphoteric  Substances. — As  mentioned 
in  the  chapter  on  ionization,  an  amphoteric  substance  is  one  that  so 
ionizes  as  to  give  both  H+  and  OH~  ions. 

Water  may  be  regarded  as  a  typical  amphoteric  substance,  since  when 
it  ionizes  at  all,  it  gives  H+  and  OH~  ions.  It  is  true  that  the  ioniza- 
tion of  water  is  very  weak,  but  there  is  no  doubt  about  its  existence,  and 
this  weakness  is  shared  by  all  amphoteric  substances.  The  weakness  in 
the  case  of  water  is  largely  due,  no  doubt,  to  the  fact  that  liquid 
water  exists  almost  entirely  as  (H20J2  and  (H2O)3,  and  not  as  simple 
H2O.  All  the  ionization  must  come,  of  course,  from  the  single  molecules. 

Amphoterism  is  a  periodic  function  of  atomic  weight.  This  has  been 
mentioned  in  the  discussion  of  the  Periodic  System.  The  elements  to 
the  left,  as  shown,  are  distinctly  basic.  As  we  go  towards  the  right,  with 
increasing  atomic  weight  the  basic  property  (the  capacity  to  give  OH~ 
ion  in  solution)  gradually  grows  less  and  the  acidic  property  (the 
capacity  to  give  H+  ion)  appears  and  increases.  We  find  this  same 
tendency  all  through  the  system.  But  the  basic  property  increases  as 
we  go  down  through  the  groups  and  extends  farther  over  in  each  suc- 
ceeding period,  so  that  pronounced  amphoteric  properties  appear  in  the 
later  periods  only  at  the  extreme  right  and  in  valences  lower  than  the 
group  valence.  Roughly  speaking,  amphoterism  begins  with  beryllium 
and  extends  to  uranium;  but  in  the  middle  of  the  system  it  broadens 
out  to  include  elements  on  either  side  of  this  line.  In  fact,  it  is  doubtful 
if  amphoterism  is  entirely  absent  in  any  element.  Thus  the  alkali  metals 
react  with  their  own  hydroxides  to  displace  hydrogen  (NaOH+Na  ~* 
*  Kuster,  Zeitschr.  Elektrochem.,  4,  117. 


EQUILIBRIUM   RELATIONS   OF  AMPHOTERIC   SUBSTANCES     259 

Na20+H),  which  makes  it  appear  as  if  NaOH  could,  under  such  drastic 
conditions,  give  a  little  H+  ion;  and  we  shall  show  later  that  even  the 
halogens  seem  to  exhibit  some  basic  ionization. 

We  have  mentioned  water  as  typically  amphoteric.  Aluminum 
hydroxide,  Al(OH)s,  is  another  example.  This  substance  is  formed  as  a 
white  gelatinous  precipitate  when  ammonium  hydroxide  is  added  to  a 
solution  of  some  aluminum  salt.  Its  amphoteric  nature  is  shown  by  the 
fact  that  it  dissolves  in  acids  to  form  aluminum  salts  (e.g.,  Aids)  or  in 
bases  to  form  aluminates  (e.g.,  NaAlO2).  Aluminum  hydroxide  ionizes 
as  follows: 

3H++A1O3S  ±^  A1(OH)3  <=* A1++++3OH-* 

An  alkali  suppresses  the  basic  ionization  and  encourages  the  acidic 
ionization.  So,  in  the  presence  of  sodium  hydroxide,  we  have  only  the 
aluminate  ion,  AlOs=.  An  acid  produces  the  opposite  result,  and  so 
in  acid  solution  we  have  only  the  aluminum  ion,  Al+++.  Ammonium 
hydroxide  cannot  take  the  place  of  sodium  hydroxide  here.  Ammo- 
nium hydroxide  is  too  weak  a  base  to  form  a  stable  salt  with  such  a 
weak  acid.  Any  such  salt  that  might  be  thus  formed  would  be 
instantly  hydrolyzed,  giving  Al(OH)s  as  a  precipitate.  If,  therefore, 
ammonium  hydroxide  is  added  to  the  acid  solution  containing  the  ion 
Al+++,  it  only  carries  the  reaction  far  enough  to  produce  aluminum 
hydroxide;  it  does  not  produce  the  aluminate  except  in  possible  traces. 
Ammonium  chloride  added  to  the  alkaline  (NaOH)  solution  removes 
the  OH~  ion  and  allows  reversal  to  A1(OH)3.  These  facts  form  the 
basis  for  the  analytical  separation  of  aluminum  from  iron. 

Chromium  hydroxide,  Cr(OH)3,  ionizes  as  does  aluminum  hydroxide, 
and  gives  the  same  reactions  with  NaOH  and  HC1.  This  is  still  weaker 
as  an  acid  than  aluminum  hydroxide.  Therefore  the  ion  CrOs^  is 
completely  hydrolyzed  in  boiling  hot  solution  to  Cr(OH)s  (distinction 
from  A1O3"). 

Hexavalent  chromium,  as  in  K2CrO4  or  K^C^O?,  is  almost  entirely 
acidic,  as  we  indicated  it  should  be.  I  Yet  it  shows  traces  of  basic 

*A11  oxygen  acids  are  hydroxides.  For  example,  sulphuric  acid  may  be  written 
SO2(OH)2.  The  acid  aluminum  hydroxide  is  usually  written  AIO(OH)  or  HA1O2, 
which  is  merely  a  partial  -anhydride  of  A1(OH)3-(A1(OH)3  -  H2O  — >  A1O  OH). 
Sulphuric  acid  may  also  be  regarded  as  a  partial  anhydride  of  S(OH)6.  (S(OH)6  — 
2H2O  — >  SO2(OH)2).  We  retain  the  fully  hydrate  form,  A1(OH)3,  for  the  sake  of 
simplicity. 

fThe  higher  positive  valences  of  any  given  element  are  always  attended  by  more 
acidic  nature  (periodic  function). 


260  COMPLEX  EQUILIBRIUM 

nature.     H2Cr04  may  be  regarded  as  the  partial  anhydride  of  Cr(OH)e, 
thus: 

Cr(OH)6-2H20->Cr02(OH)2  or  H2Cr04 

Keeping  the  hydrated  form,  the  ionization  may  be 


We  have  seen  under  "  Oxidation  "  that  Cr+"  +  in  K2Cr2O7  (or  K2Cr04) 
changes  to  Cr+++  when  it  acts  as  an  oxidant;  and  it  is  a  well-known 
fact  that  this  oxidation  proceeds  much  more  readily  in  an  acid  solution. 
This  is  due,  no  doubt,  to  the  encouragement  of  the  basic  ionization  (as 
seen  on  the  right  above),  giving  more  of  the  hexavalent  chromium  ion. 
In  neutral  solution  this  basic  ionization  is  almost  absent  because  the 
tendency  in  this  case  is  almost  entirely  acidic. 

Iron  is  not  amphoteric  at  all  in  its  bivalent  form,  and  it  shows  noth- 
ing more  than  traces  of  amphoterism  in  its  trivalent  form.  It  may, 
however,  be  oxidized  to  an  unstable  hexavalent  ion,  FeO4=,  in  which  it 
is  mainly  acidic,  but  perhaps  faintly  basic  also.  Salts  of  this  ion  can  be 
prepared,  such  as  Na2FeO4  (sodium  ferrate),  which  are  analogous  to 
the  chromates  and  sulphates. 

In  their  positive  valences,  as  seen  for  example  in  HC1O,  HC102, 
HClOs,  etc.,  the  halogens  follow  the  rule  as  to  acidity,  those  of  higher 
valence  being  more  acidic.  Thus,  HClOs  is  a  much  stronger  acid  than 
HC1O.  In  these  cases  also,  a  slight  amphoteric  nature  appears,  as  the 
following  example  seems  to  show: 

It  is  a  well-known  fact  that  iodine  displaces  Br  from  HBrOs*  or 
KBrOs.  This  reaction  proceeds  much  more  rapidly  in  presence  of  an 
acid  (e.g.,  H2SO4),  a  fact  which  is  undoubtedly  due  to  the  encourage- 
ment of  basic  ionization,  as  with  chromium.  HBrOs  may  be  regarded 
as  a  partial  anhydride  form  of  Br(OH)5.  (Br(OH)5— 2H2O  ->  Br02OH 
or  HBrOs)  •  The  hydrated  form  may  ionize  thus : 


5H++BrO5"  t>  Br(OH)5  <=*  Br+      +50H~ 

Ordinarily  there  is  scarcely  a  trace  of  the  basic  ionization  as  seen  on  the 
right,  and  therefore  no  Br++  to  displace.  In  the  presence  of  an  acid  the 
basic  ionization  is  encouraged,  giving  more  of  the  pentavalent  ion. 
Displacement  can  then  proceed  rapidly  as  noted  above. 

*  Where  the  halogens  are  negative  fluorine  is  the  most  negative;  but  where  they 
are  positive,  iodine  is  the  most  positive. 


EXERCISES 


261 


Potassium  permanganate  and  nitric  add  may  be  mentioned  as  two 
other  common  reagents  in  which  amphoterism  and  consequent  basic 
ionization  are  probably  exhibited.  Permanganic  acid,  HMn04,  is  the 
partial  anhydride  of  the  heptavalent  hydroxide,  Mn(OH)7.  In  the 
presence  of  an  acid  this  may  therefore  give  the  heptavalent  manganic 
ion.  This  is  in  line  with  the  fact  that  permanganate  is  a  much  more 
powerful  oxidant  in  acid  than  in  neutral  solution. 

Nitric  acid  -may  be  regarded  as  the  partial  anhydride  of  the  penta- 

valent  hydroxide,  N(OH)5,  and  may  in  the  presence  of  a  strong  acid 

+++ 
give  the  pentavalent  nitrogen  ion,  N+"   .     Our  evidence  for  this  is  the 

fact  that  the  nitrate  ion  alone,  as  seen  for  example  in  a  neutral  solution 
of  KNOs,  does  not  act  as  an  oxidizing  agent,  while  in  presence  of  an 
acid  it  does  thus  act.  According  to  our  theory,  the  acid  encourages 
the  basic  ionization,  thus  bringing  out  the  pentavalent  nitrogen  ion. 
The  action  of  hydrochloric  acid  on  nitric  acid  is  also  in  line  with  our 
theory  of  amphoterism.  The  products  of  the  reaction  are  nitrosyl 
chloride,  NOC1,  and  chlorine  gas,  C12;  and  to  produce  these  it  is  prob- 
able that  the  reaction  proceeds  in  two  steps,  the  oxy-chloride, 
N(OH)2C13,  being  first  formed  and  this  then  breaking  down  into  nitrosyl 
chloride  and  chlorine,  thus : 

N(OH)5+3HC1  -»  N(OH)2C13+3H2O 

N(OH)2C13  -» NOC1+C12+H2O* 


EXERCISES 

1.  Using  silver  acetate  as  an  example,  develop  the  solubility-product  principle. 

2.  Calculate  from  the  following  data  the  solubility  product  of  the  given  substances : 


Solubility  in  grams 
per  Liter. 

Ionization 
(Per  Cent). 

AgCl  
PbCl2  
Mg(OH)2  
:  CaSO4  

0.0017 
19.46 
0.009 
2  0 

100 
80 
100 
54 

3.  Give  the  "  rule  for  precipitation." 

4.  What  is  the  effect  of  foreign  salts  on  the  solubility  product? 
6.  What  is  the  "  rule  for  solution  of  precipitates  "? 

*  For  further  application  of  this  theory  regarding  basic  ionization  of  amphoteric 
substances,  see  Stieglitz,  Qual.  Anal.,  Vol.  I,  p.  249.  See  also  McCay,  Jour.  Am. 
Chem.  Soc.,  24,  661  (1902). 


262  COMPLEX  EQUILIBRIUM 

6.  How  can  we  tell  whether  a  so-called  "  insoluble  salt  "  will  dissolve  in  an  acid? 
Example. 

7.  Will  carbonic  acid  precipitate  calcium  from  the  chloride?     Why?    Will  sodium 
carbonate?     Why?     (Work  out  the  data  for  carbonic  acid  and  saturated  CaCl2.) 

8.  Will  carbonic  acid  ever  precipitate  a  carbonate?     Explain  with  an  example. 

9.  Write  equilibria  and  explain  the  solution  of  calcium  carbonate  in  hydrochloric 
acid. 

10.  Show  exactly  what  happens  when  H2S  is  passed  into  a  zinc  sulphate  solution — 
how  to  secure  complete  precipitation,  etc. 

11.  Explain  all  the  necessary  conditions  for  securing  complete'  separation  of  the 
copper  group  from  the  zinc  group. 

12.  Do  all  sulphides  dissolve  in  hydrochloric  acid?     Why? 

13.  Trace  all  the  effects  seen  when  ammonium  hydroxide  is  added  to  a  solution 
of  some  magnesium  salt.     What  if  ammonium  chloride  is  added  beforehand? 

14.  Why  is  ammonium  chloride  added  before  precipitating  the  aluminum  group 
with  ammonia?     Why  does  it  not  prevent  the  precipitation  of  the  members  of  this 
group? 

15.  What  complex  ion  does  silver  form  with  ammonia?     Is  it  soluble?     Give  its 
dissociation  constant.       What  is  the  effect  of  increasing  the  concentration  of  NH3? 
What  are  the  reactions  by  which  it  is  formed  from  AgNO3?     How  is  it  manipulated 
in  separating  Cl~,  Br~~,  and  I~? 

16.  Describe  the  copper-ammonium  complex,  giving  preparation,  color,  stability, 
etc. 

17.  Describe  the  cyanide  complex  of  silver. 

18.  Describe  the  cupro-cyanide  and  the  cadmi-cyanide  complexes  and  their  use  in 
analysis? 

19.  Describe  the  equilibrium  relations  of  the  ferric-oxalate  complex. 

20.  What  is  Fehling's  solution?     Formula? 

21.  Give  formula  and  properties  of  a  complex  lactate  of  iron. 

22.  What  is  an  amphoteric  substance?     What  amphoteric  properties  has  water? 

23.  Show  the  periodic  relations  of  amphoterism. 

24.  Give  the  equilibrium  relations  of  A1(OH)3. 

25.  What  is  meant  by  "  partial  anhydrides  "  of  hydroxides?     Examples. 

26.  Explain  the  amphoteric  nature  of  chromium  in  both  its  trivalent  and  hexa- 
valent  forms. 

27.  To  what  extent  is  iron  amphoteric? 

28.  Explain  the  amphoteric  tendencies  of  the  halogens. 

29.  Point  out  the  amphoteric  nature  of  manganese  in  KMnC>4  and  of  nitrogen  in 
HNO3. 


CHAPTER  XIX 
ELECTROCHEMISTRY 

Electrical  Units  and  their  Measurements. — (a)  Quantity. — The 
unit  quantity  of  electricity  is  the  coulomb.  This  is  the  quantity  which, 
when  run  through  a  solution  of  a  silver  salt,  deposits  or  plates  out 
0.001118  gm.  of  silver.  The  coulomb  is  one-tenth  of  one  electromag- 
netic unit. 

(6)  Flow. — The  rate  at  which  a  current  of  electricity  passes  through  a 
conductor  is  measured  in  amperes.  When  a  coulomb  passes  through  a 
conductor  in  one  second  the  current  is  said  to  be  1  ampere. 

When  a  current  passes  through  a  wire  a  magnetic  field  is  developed 
around  it.  Imagine  a  current  flowing  along  a  wire  from  the  eye  to  this 
page.  Under  these  conditions  the  magnetic  lines  of  force  pass  around 
the  wire  in  a  clockwise  direction.  This  really  means  that  the  north  pole 
of  a  magnet,  if  placed  in  the  field,  would  be  drawn  around  the  wire  in  a 
clockwise  direction.  The  force  with  which  such  a  pole  would  be 
attracted  is  proportional  to  the  current  flowing  through  the  wire.  If  the 
wire  is  bent  in  the  shape  of  a  coil  lying  flat  on  the  page  and  a  current 
passes  around  the  coil  clockwise,  a  north  magnetic  pole  will  be  drawn 
through  the  coil  towards  the  page.  If  the  magnet  is  fixed  and  the  coil 
free  to  move,  the  latter  will  move;  but  the  relative  movement  will  be 
the  same  as  that  described  above.  The  final  result  in  either  case  will  be 
such  as  to  cause  a  magnetic  needle  placed  at  the  center  of  the  coil  to 
stand  with  its  north  pole  pointing  away  from  the  eye.  The  coil  itself, 
with  the  current  passing  through  it,  may  be  thought  of  as  a  magnet,  its 
north  pole  being  the  side  where  the  lines  of  force  emerge.  If  such  a 
coil  be  placed  in  a  magnetic  field  whose  lines  of  force  do  not  coincide 
with  its  own,  it  will  tend  to  move  or  cause  the  magnet  to  move  so  that 
the  lines  of  force  will  coincide. 

Instruments,  based  upon  the  above  facts,  have  been  devised  for 
measuring  electric  currents.  In  one  form  of  instrument  a  movable 
magnetic  needle  is  placed  near  the  center  of  a  coil,  but  in  such  a  position 
that  its  lines  of  force  do  not  coincide  with  these  of  the  coil  (see  Fig.  35). 
When  a  current  passes  through  the  coil,  the  magnet  rotates  on  its  axis 

263 


264 


ELECTROCHEMISTRY 


FIG.  35. — Principle 
of  the  Ammeter. 


and  this  causes  a  hand  to  move  over  a  scale  against  the  action  of  a  spring. 
If  the  scale  is  uncalibrated  the  instrument  is  called  a  "  galvanometer  "; 
if  calibrated  it  is  called  an  "  ammeter."  In  another  form  of  instrument 
(the  d' Arson val  type),  the  magnet  is  of  horseshoe 
shape  and  is  fixed.  The  coil  is  placed  between 
its  poles  in  such  a  position  that  the  lines  of  force 
developed  by  the  current  do  not  coincide  with 
those  of  the  magnet.  It  therefore  rotates  when 
a  current  is  passed,  acting  against  the  force  of 
a  hair  spring,  as  in  the  other  form  of  instrument. 
In  this  type  of  instrument  the  coil  consists  of 
many  turns  of  fine  wire,  and  to  permit  the 
current  to  pass  unobstructed,  a  shunt  is  pro- 
vided. The  sketch  will  show  the  arrangement  of 
the  parts.  (See  Fig.  36.) 

Note  that  part  of  the  current  flows  through  the  shunts  while  a  part 
flows  through  the  coil.  If  more  shunt  wires  are  added  more  of  the 
current  will  be  turned  off  from  the  coil,  and  therefore  a  larger  total  cur- 
rent in  the  circuit  will  be  required  to  give  the  same  deflection.  If  the 
shunts  are  thus  increased  so  that  ten  times  the  original  current  is 
required  for  the  same  deflection,  the  ammeter  can  be  used  for  a  ten-fold 
higher  range.  Ammeters  are  often 
equipped  with  several  calibrated 
shunts  which  can  be  used  to  alter  the 
range  at  will. 

The  d' Arson val  galvanometer  is 
built  on  the  same  principle  as  the 
ammeter,  but  has  a  small  mirror  at- 
tached to  the  coil  in  place  of  the  hand. 
In  front  of  the  mirror  is  placed  a 
scale,  and  the  image  of  the  latter  is 
viewed  in  the  mirror  by  means  of  a 
small  telescope.  Any  rotation  of  the 
mirror  causes  the  image  to  swing  off  to 
one  side;  and  because  of  the  consider- 
able distance  between  the  scale  and 

the  mirror,  any  such  rotation  is  highly  magnified,  making  it  possible 
to  note  the  presence  of  exceedingly  small  currents. 

(c)  Resistance. — Conductors,  while  allowing  the  passage  of  the  cur- 
rent, offer  a  certain  amount  of  resistance,  depending  on  the  material 
of  which  they  are  constructed  and  also  on  their  dimensions.  The  unit 
of  resistance  is  the  ohm.  This  is  equal  to  the  resistance  offered  by  a 


FIG.  36. — The  Ammeter. 


ELECTRICAL  UNITS  AND  THEIR   MEASUREMENTS          265 

column  of  pure  mercury  106.3  cm.  long  and  1  mm.  in  cross-section  at 
0°  C.  Such  a  column  weighs  14.4521  gm. 

Resistance  is  proportional  to  the  length  of  the  conductor  and 
inversely  proportional  to  its  cross-section.  Thus,  if  a  wire  1  foot  long 
has  a  resistance  of  1  ohm,  2  feet  of  the  same  wire  will  have  a  resistance 
of  2  ohms.  On  the  other  hand,  if  a  wire  of  1  sq.  mm.  cross-section  has  a 
resistance  of  1  ohm,  another  wire  of  the  same  material  and  same  length, 
but  of  2  sq.  mm.  cross-section,  will  have  a  resistance  of  only  J  ohm. 

Specific  resistance  is  the  resistance  of  a  centimeter  cube  of  a  given 
substance.  Notice  the  phrase  "  centimeter  cube."  The  term  "  cubic 
centimeter  "  refers  simply  to  volume  without  designating  the  shape. 
A  wire  of  cross-section  1  sq.  mm.,  and  100  cm.  long  has  a  volume  of  1 
cu.  cm.,  but  is  not  a  "  centimeter  cube."  If  the  resistance  of  a  centi- 
meter cube  (the  specific  resistance)  of  a  substance  is  1,  the  resistance  of 
such  a  wire  of  the  same  material  would  be  10,000.  (Prove  this  by  the 
last  paragraph.) 

The  ease  with  which  a  substance  conducts  is  called  its  conductivity, 
and  this  is  measured  in  reciprocal  ohms  (sometimes  called  "  mohs  "). 
Thus,  if  the  resistance  of  a  certain  conductor  is  1  ohm,  its  conductivity 
is  1.  If  the  resistance  is  10  ohms,  the  conductivity  is  1/10.  Specific 
conductivity  is  the  conductivity  of  a  centimeter  cube  of  a  substance. 

Resistance  may  be  measured  by  means  of  an  instrument  called 
"  Wheatstone's  bridge."  The  principle  of  this  instrument  can  be 
understood  from  the  diagram  and  description  of  Fig.  37. 


d 

FIG.  37. — Diagram  of  Wheatstone's  Bridge. 

If  the  terminals  of  a  battery  are  connected  at  A  and  B,  there  will  be  a 
certain  fall  in  potential  between  these  points.  The  fall  in  both  branches, 
A  EB  and  AcB,  will,  of  course,  be  the  same.  The  rate  of  fall  along  either 
branch  is  proportional  to  the  resistance.  If,  therefore,  we  select  a  point 
E  between  the  known  resistance  R  and  the  unknown  resistance  x,  and 
connect  through  the  galvanometer  G  with  a  point  on  the  wire  acd,  a 
current  may  or  may  not  flow  through  the  galvanometer,  depending  on 
the  point  of  contact,  c.  If  c  is  selected  so  that  no  current  flows,  the 
potential  of  E  and  c  must  be  the  same,  and  then  it  follows  that 

x  :  R : :  ac  :  cd;  and  x  =  R  ac/cd. 


266  ELECTROCHEMISTRY 

In  case  we  wish  to  determine  the  resistance  of  a  solution,  where  a 
direct  current  would  cause  decomposition,  an  alternating  current  is  used ; 
and  since  a  galvanometer  cannot  be  used  with  an  alternating  current,  a 
telephone  receiver  is  substituted.  This  gives  a  humming  sound  when  a 
current  passes. 

(d)  Potential  or  Electromotive  Force. — If  conductors  offer  resistance 
to  the  passage  of  the  current,  a  certain  amount  of  electrical  pressure  or 
potential  is  necessary  to  force  the  current  through  them.     This  pressure 
is  called  "  electromotive  force  "  (abbreviated  to  E.M.F.),  and  is  meas- 
ured in  volts.     The  volt  is  the  E.M.F.  required  to  maintain  a  current  of 
1  ampere  against  a  resistance  of  1  ohm. 

E.M.F.  is  usually  measured  by  means  of  an  instrument  called  a 
voltmeter.  The  construction  of  a  voltmeter  is  exactly  like  that  of  an 
ammeter,  except  that  it  is  always  so  arranged  as  to  have  a  very  high 
resistance  and  thus  permit  the  passage  of  only  a  very  small  amount  of 
current.  In  the  movable  magnet  type  of  instrument  this  is  accomplished 
by  giving  the  coil  a  very  large  number  of  turns  of  fine  wire.  In  the 
d'Arsonval  instrument  the  same  thing  is  accomplished  by  increasing  the 
resistance  of  the  shunt,  the  coil  always  having  a  high  resistance. 

An  ammeter  is  connected  in  such  a\way  that  the  whole  of  the  current 
used  passes  through  the  instrument,  very  little  resistance  being  offered. 
This  is  what  is  called  "  connecting  in  series."  A  voltmeter,  on  the  other 
hand,  is  always  placed  upon  a  side  circuit  connected  between  the  two 
points  on  the  main  circuit  whose  difference  of  potential  is  to  be  meas- 
ured. It  is  said  to  be  "  connected  in  shunt." 

E.M.F.  may  also  be  measured  by  means  of  an  instrument  called  a 
"  potentiometer,"  used  in  conjunction  with  a  standard  cell  of  known 
potential.  The  potentiometer  is  really  a  modified  form  of  Wheat- 
stone's  bridge. 

(e)  Ohm's  Law. — The  current  which  flows  through  any  circuit  is 
proportional  to  the  E.M.F.  and  inversely  proportional  to  the  resistance. 
This  is  called  "  Ohm's  Law."     If  a  certain  current  is  flowing  and  we 
double  the  potential,  the  current  is  doubled.     If  we  double  the  resistance 
the  current  is  halved.     The  facts  of  Ohm's  Law  can  be  put  into  the  sim- 
ple mathematical  equation 

C  =  E/R 

where    C=  current,    E=  potential,    and    E  =  resistance.     In    terms    of 
amperes,  volts,  and  ohms,  this  becomes 

volts 
amperes  = 


ohms 


ELECTRICAL  UNITS  AND   THEIR   MEASUREMENTS  267 

If  any  two  of  the  factors  of  Ohm's  Law  are  known,  the  third  may 
be  calculated.  Thus,  resistance  may  be  measured  by  means  of  a  volt- 
meter and  ammeter  connected  as  in  the  sketch  above.  From  Ohm's 
law,  R  =  E/C.  Therefore,  all  we  need  to  do  is  to  connect  an  ammeter  in 
series  with  the  resistance  to  be  measured  and  have  a  voltmeter  in  shunt 
around  its  terminals.  The  necessary  data  can  then  be  read  off. 

For  the  regulation  of  the  current  flow  it  is  often  necessary  to  intro- 
duce into  the  circuit  a  variable  resistance.  Such  variable  resistances 
are  seen  in  various  forms.  They  are  called  "  rheostats."  The  essen- 
tial feature  is  a  rather  long  wire  of  high  resistance  wound  on  a  bar  or 
cylinder  of  non-conducting  material  so  that  the  coils  do  not  touch.  A 
sliding  contact  is  provided  which  makes  it  possible 
to  include  in  the  circuit  as  much  of  the  coil  as  is 
necessary  to  give  the  proper  resistance. 

The  sketch  (Fig.  38)  shows  in  diagrammatic 
form  the  arrangement  of  the  parts.  The  current 
must  pass  through  the  arm  A,  and  then  through 
that  part  of  the  coil  which  lies  between  the  arm 
and  the  binding  post  B.  The  arm  may  be  moved 
to  any  point,  A',  including  any  desired  length  of 
the  coil. 

Rheostats  are  constructed  for  a  definite  cur-  FlG-  38-~Dia^am  °f  a 
rent  range,  and  they   should    not    be  used    be- 
yond this  range.     In    general,  when    the    total 

resistance  is  large,  the  current  capacity  is  small,  and  vice  versa.  To  get 
high  resistance  the  coil  is  made  of  small  wire;  and  if  a  heavy  current 
were  used  this  wire  would  be  overheated,  and  perhaps  even  melted  or 
burned.  When  the  total  resistance  of  the  instrument  is  low,  a  large 
wire  with  high  conducting  capacity  is  used.  The  range  is  usually 
marked  on  the  instrument,  and  care  should  be  exercised  to  note  this 
before  the  instrument  is  used. 

Power  and  Work. — The  practical  unit  of  electrical  power  is  the  watt, 
which  may  be  defined  as  the  power  delivered  by  a  current  of  1  ampere 
under  an  E.M.F.  of  1  volt.  If  the  voltage  is  2  and  the  current  1  ampere, 
the  power  delivered  is  2  watts;  if  the  current  is  2  amperes,  and  the  volt- 
age 1,  the  power  is  2  watts.  In  general,  then,  watts  =  volts  X  amperes. 
A  kilowatt  is  obviously  1000  watts. 

If  the  watt  is  merely  potential  times  current,  it  represents  merely 
the  rate  at  which  work  is  being  done;  and  the  amount  of  work  actually 
done  depends  on  the  length  of  time  over  which  this  rate  is  continued. 
In  buying  or  selling  electrical  power,  therefore,  it  is  customary  to  reckon 
the  service  in  terms  of  watt-hours,  or,  for  large  amounts,  in  kilowatt 


268  ELECTROCHEMISTRY 

hours.  The  kilowatt-hour  meter,  or  "  watt  meter/'  as  it  is  usually 
called,  is  only  a  special  form  of  motor,  and  is  so  constructed  as  to  register 
on  its  dials  the  work  done  on  the  circuit  in  terms  of  kilowatt-hours. 
When  power  has  been  delivered  for  one  hour  at  the  rate  of  1000  watts 
the  instrument  points  to  "  1  "  on  its  dial,  meaning  that  1  kilowatt-  hour 
of  work  has  been  done. 

Electrical  apparatus  is  usually  graded  in  terms  of  wattage,  or  power 
consumption.  Thus  we  speak  of  a  60-watt  tungsten  lamp,  or  a  75- 
watt  motor,  or  a  550-watt  flat-iron.  It  is  interesting  to  note  the  meaning 
of  this  sort  of  grading  in  terms  of  efficiency.  Thus,  an  ordinary  tung- 
sten lamp  delivers  about  1  candle-power  of  light  for  every  1.25  watts, 
so  that  a  60-watt  lamp  gives  about  48  candle-power.  The  old  carbon- 
filament  lamps  took  about  3.5  watts  per  candle-power,  and  were,  there- 
fore, only  about  one-third  as  efficient.  A  horse-power  is  746  watts. 
Therefore,  to  determine  the  horse-power  of  a  motor,  divide  the  wattage 
by  746.  Note  that  a  motor  which  draws  a  kilowatt  is  about  1|  H.P. 
At  the  rate  quite  common  now,  this  motor  would  cost  12  cents  per  hour 
to  run.  Note,  however,  the  large  amount  of  work  done  for  the  money. 
A  flat-iron  uses  about  550  watts,  which  is  about  three-fourths  of  one 
horse-power.  It  is  interesting  to  note  that  if  an  average  horse  were 
attached  to  some  mechanical  device  which  could  convert  all  his  muscular 
energy  into  electrical  energy  he  would  have  about  all  he  could  do  to  run 
one  flat-iron.  This  is  only  typical  of  what  is  always  the  case  when 
electrical  energy  is  converted  into  heat.  The  power  required  to  run 
one  flat-iron  would  run  six  vacuum  cleaners  and  would  light  a  fair-sized 
house. 

If  we  desire  to  know  what  current  is  flowing  in  a  machine  or  device 
whose  wattage  is  known,  we  have  only  to  divide  watts  by  volts.  Thus 
a  550-watt  flat-iron,  running  on  an  ordinary  110-volt  house  circuit 
draws  550/110  or  5  amperes. 

Faraday's  Laws  *  of  Electrolysis. — When  a  direct  current  is  passed 
through  the  solution  of  an  electrolyte,  the  electrolyte  is  decomposed, 
and  the  products  of  the  decomposition  are  found  at  the  respective  elec- 
trodes. The  object  of  this  section  is  to  show  the  quantitative  relation- 
ship existing  between  this  decomposition  and  the  electric  current  which 
causes  it. 

When  studying  this  matter  in  1834,  Faraday  discovered  that  if  the 
same  strength  of  current  were  used  and  the  process  allowed  to  continue 
for  the  same  length  of  time,  successive  experiments  with  the  same  elec- 
trolyte always  gave  the  same  amount  of  decomposition.  This  fact  he 
embodied  in  what  is  termed  his  "  First  Law,"  viz.:  The  weight  of  any 
*  Expr.  Researches,  III.,  Ser.  No.  373  (1832). 


FARADAY'S  LAWS  OF  ELECTROLYSIS 


269 


substance  liberated  at  one  of  the  electrodes  during  electrolysis  is  proportional 
to  the  quantity  of  electricity  passed  through  the  electrolytic  cell.  For  exam- 
ple, if  a  current  of  1  ampere  is  passed  through  a  solution  of  any  silver 
salt — nitrate,  sulphate,  or  acetate — for  one  hour,  4.025  gm.  of  silver  will 
be  deposited.  This  is  in  line  with  our  definition  of  "  coulomb,"  for  a 
current  of  1  ampere  for  one  hour  (3600  seconds) ,  means  the  passage  of 
3600  coulombs  of  electricity;  and,  since  the  coulomb  is  by  definition  the 
quantity  required  for  the  deposition  of  0.001118  gm.  of  silver,  3600  cou- 
lumbs  should  deposit  3600X0.001118  gm.,  or  4.025  gm.  of  silver.  This 
law  is  absolutely  independent  of  conditions  of  temperature,  dilution, 
and  current  strength.  Thus,  if  the  current  is  one-half  ampere,  the 
deposition  of  4.025  gm.  of  silver  will  require  two  hours,  but  this  gives 
the  same  quantity  of  electricity,  viz.,  7,200X1/2,  or  3600  coulombs. 

In  the  second  place,  Faraday  found  that  when  he  passed  a  current 
through  several  electrolytic  cells  connected  in  series,  the  quantities  of 
the  substances  liberated  were  exactly  porportional  to  their  equivalent  weights. 
This  is  called  Faraday's  "  Second  Law."  Suppose,  for  example,  we 
have  the  series  of  cells  shown  in  the  following  sketch  (Fig.  39).  If  we 


FIG.  39.— Electrolytic  Cells. 

allow  the  current  to  pass  through  such  a  series  until  8  gm.  of  oxygen  are 
liberated  in  cell  1,  and  then  stop  the  action,  we  shall  find,  if  we  have 
collected  the  other  products  of  electrolysis,  that  1.008  gm.  of  hydrogen 
are  liberated  in  this  same  cell.  In  cell  2,  we  shall  get  31.8  gm.  of  copper 
and  35.45  gm.  of  chlorine  gas;  in  cell  3,  we  shall  get  107.88  gm.  of 
silver  and  8  gm.  of  oxygen;  and  in  cell  4,  we  shall  get  32.7  gm.  of  zinc 
and  70.92  gm.  of  bromine.  These  are  the  equivalent  weights  of  the 
elements  concerned. 

As  in  the  case  of  the  first  law,  so  here,  it  makes  no  difference  whether 
the  current  is  large  or  small  or  whether  the  solutions  are  concentrated 
or  dilute,  the  proportions  of  the  substances  liberated  are  as  indicated. 
If,  during  the  process,  we  suddenly  make  one  solution  more  concentrated 


270  ELECTROCHEMISTRY 

by  adding  more  of  the  solid,  the  resistance  will  thereby  be  decreased  at 
this  point,  making  the  total  resistance  of  the  circuit  less.  This  will  only 
operate  to  increase  the  current  in  like  degree  in  every  part  of  the  circuit, 
and  thus  cause  a  like  increase  in  the  rate  at  which  the  different  substances 
are  liberated,  but  the  same  proportions  will  still  hold. 

If  1  coulomb  of  electricity  deposits  0.001118  gm.  of  silver,  the  depo- 
sition of  1  gm.  equivalent  will  require  107.88/0.001118  or  96,500  cou- 
lombs. But  according  to  Faraday's  second  law,  just  discussed,  it 
follows  that  the  same  quantity  of  electricity  will  deposit  or  liberate  1 
gram  equivalent  of  any  element.  In  honor  of  the  great  electrical 
pioneer,  this  quantity  of  electricity  has  been  named  the  "  faraday." 

Basis  for  Faraday's  Laws. — We  have  explained  chemical  combination 
in  terms  of  the  electron  theory  by  supposing  that  in  the  case  of  a  polar 
compound  one  or  more  electrons  pass  across  from  a  positively  inclined 
atom  to  a  negatively  inclined  atom,  causing  the  two  atoms  to  become 
oppositely  charged,  and  that  the  atoms  are  then  held  together  by  elec- 
trostatic attraction.  We  have  seen  that  the  valence  of  an  element  is 
probably  governed  by  the  number  of  electrons  a  single  atom  is  able  to 
give  up  or  take  on.  Change  of  valence  we  have  also  explained  as  a  giv- 
ing up  or  taking  on  of  electrons,  oxidation  being  the  former  and  re- 
duction the  latter.  Again,  ionization  in  solution  has  been  explained 
by  reasoning  that  a  solvent  of  high  dielectric  comes  between  the 
charged  atoms  or  radicals  of  a  compound  and  renders  them 
more  or  less  electrically  indifferent  to  each  other.  From  this  we 
have  shown  that  ions  are  to  be  regarded  merely  as  charged  atoms  or 
radicals,  the  magnitude  of  the  charge  being  governed  by  the  number  of 
electrons  gained  or  lost  at  the  moment  of  combination.  Every  ion, 
therefore,  carries  either  the  electronic  charge,  1.6X10"20  electro- 
magnetic units,  or  some  multiple  of  this.  Since  a  coulomb  is  one- 
tenth  of  one  electromagnetic  unit,  the  charge  carried  by  a  univalent 
ion  is  1.6X10"19  coulombs. 

If  we  keep  these  facts  in  mind,  the  laws  of  electrolysis  almost  explain 
themselves.  When  two  oppositely  charged  electrodes  are  placed  in  a 
solution  all  the  positive  ions  are  immediately  attracted  towards  the 
cathode,  and  all  the  negative  ions  towards  the  anode.  Suppose  the  cation 
is  copper:  each  copper  ion  carries  two  unit  charges  of  "•  positive  elec- 
tricity," viz.,  3.2X10"19  coulombs.  Being  attracted  by  the  cathode, 
these  copper  ions  move  towards  it,  and  upon  coming  in  contact  with  it, 
each  receives  2  electrons.  Becoming  thus  neutral  atoms  of  copper,  they 
attach  themselves  to  the  cathode,  forming  a  coating  of  pure  copper. 
Since  all  the  copper  ions  are  of  the  same  mass  and  each  one  carries  the 
same  charge,  it  follows  that  any  given  quantity  of  metal,  upon  plating 


ELECTRODE   REACTIONS  271 

out,  will  discharge  the  same  quantity  of  electricity.  The  case  of  the 
anion  is  similar.  Suppose  it  to  be  chlorine.  Each  chlorine  ion  carries 
one  unit  charge,  of  negative  electricity,  viz.,  1.6X10"19  coulombs. 
In  discharging,  the  chlorine  ions  give  up  their  extra  electrons,  becoming 
neutral  atoms,  and  these  then  unite  into  pairs  (molecules)  by  the  shar- 
ing process.  Thus  Faraday's  first  law  is  explained. 

From  these  same  considerations  Faraday's  second  law  follows  at 
once.  If  the  copper  ion  carries  a  double  charge  and  the  chlorine  ion  a 
single  charge,  then  for  every  atomic  weight  of  copper  discharging  at  the 
cathode,  two  atomic  weights  of  chlorine  must  discharge  at  the  anode. 
Otherwise  the  solution  could  not  remain  neutral,  as  it  really  does. 
But  one  atomic  weight  of  copper  contains  two  equivalents  and  two 
atomic  weights  of  chlorine  contain  two  equivalents.  These  are  the 
proportions  called  for  by  Faraday's  second  law. 

Electrode  Reactions. — In  the  light  of  the  above  discussion  it  will  be 
noted  at  once  that  there  are  just  two  types  of  reaction  concerned  in 
electrolysis:  at  the  cathode,  reduction,  the  taking  on  of  electrons:  at 
the  anode,  oxidation,  the  giving  off  of  electrons.  We  have  only  to  show 
in  what  ways  these  reactions  may  take  place. 

The  reducing  action  at  the  cathode  may  occur  in  several  ways : 

(a)  A  positive  ion  may  discharge  completely.  Thus  the  cation 
Cu++  may  take  on  2  electrons  and  plate  out  as  metallic  copper,  Cu. 

(6)  A  polyvalent  cation  may  discharge  but  partially.  Thus  Cu++ 
may  take  on  1  electron  and  remain  in  solution  as  the  univalent,  or 
cuprous,  ion,  Cu+.  The  same  thing  can  occur  with  Fe+++. 

(c)  An  anion  may  be  formed.  Thus,  molecular  iodine,  12,  may  be 
changed  to  iodide  ion,  I~. 

In  any  of  these  cases  certain  complications  may  arise  and  somewhat 
change  the  course  of  the  reaction,  but  in  the  end  it  is  sure  to  be  some  form 
of  reduction.  Note  the  following  examples: 

When  we  electrolyze  a  compound  of  any  metal  which  in  the  free 
state  can  react  with  water  to  displace  hydrogen  (e.g.,  Na,  K,  Ca,  Mg), 
the  metal  does  not  plate  out  (unless  we  use  a  mercury  cathode,  in  which 
case  an  amalgam  is  formed) ,  but  hydrogen  escapes  instead,  and  hydroxyl 
ions  are  found  to  accumulate  around  the  cathode  together  with  the  ions 
of  the  metal;  in  other  words,  the  cathode  liquid  becomes  alkaline. 

Two  theories  have  been  offered  in  explanation.*  According  to  the 
old  theory,  the  metal  first  discharges  and  then  reacts  with  water,  thus: 

2Na+H2O  ->  2Na++2OH-+H2 
*  LeBlanc,  Electrochemistry,  pp.  302-308. 


272  ELECTROCHEMISTRY 

This  is  spoken  of  as  a  "  secondary  reaction,"  meaning  that  the  hydrogen 
does  not  come  directly  as  a  product  of  electrolysis.  According  to  the  new 
theory,  hydrogen  ion,  already  present  from  the  water,  discharges  and 
leaves  behind  the  corresponding  OH~,  also  from  the  water.* 

Where  low  currents  are  used  the  new  theory  undoubtedly  has  the 
advantage;  for,  where  two  positive  ions  are  present,  that  one  will  cer- 
tainly be  discharged  which  has  the  lesser  tendency  to  remain  in  the  ionic 
condition.  That  hydrogen  has  less  than  sodium  and  such  metals  is 
proved  by  the  fact  that  these  metals  are  able  to  go  into  the  ionic  condi- 
tion and  drive  hydrogen  out,  that  is,  are  able  to  displace  hydrogen  from 
water.  But  we  must  remember  that  the  concentration  of  H+  ion,  small 
at  the  start,  is  constantly  growing  smaller  on  account  of  the  accumula- 
tion of  OH~  ion;  and  so,  in  the  rush  and  hurry  caused  by  heavy  cur- 
rents, it  is  possible  that  the  metals  do  discharge  also,  and  then  react 
with  water  at  their  leisure. 

If  some  substance  is  electrolyzed  which  ordinarily  would  give  hydro- 
gen gas  at  the  cathode,  and  at  the  same  time  some  oxidizing  ion,  like 
MnO4~  or  Cr2O7=,  is  present,  no  hydrogen  will  be  evolved.  If  dis- 
charged at  all,  it  is  instantly  used  up  in  reducing  the  oxidizing  ion.  In 
some  cases  the  oxidizing  ion  is  reduced  directly  by  taking  up  the  elec- 
trons necessary  to  the  passage  of  the  current;  in  others,  hydrogen  is,  no 
doubt,  discharged.  Nitric  acid,  for  example,  is  reduced  to  ammonia, 
which,  of  course,  requires  hydrogen,  thus : 

HNO3+8H  ->  NH3+3H2O 

The  oxidizing  action  at  the  anode  may  also  occur  in  several  ways: 

(a)  An  anion  may  discharge  by  giving  up  electrons.  Thus  iodide 
ion,  I~,  becomes  molecular  iodine  in  the  same  manner  as  described 
for  chlorine  above.  Note  that  this  is  the  exact  reverse  of  the  action  at 
the  cathode. 

(6)  A  cation,  or  the  central  element  in  an  anion,  may  be  oxidized. 
Thus,  ferrous  ion  is  changed  to  ferric,  or  tetravalent  sulphur  in  S0s=  is 
changed  to  hexavalent  sulphur  in  864 =. 

(c)  A  cation  may  be  formed.  Thus,  if  the  anode  is  of  some  material 
which  readily  forms  ions — say  zinc — the  anion  will  not  discharge  at  all, 
but  instead  neutral  atoms  of  the  metal  lying  at  the  surface  of  the  anode 
will  give  up  electrons  to  the  conductor  and  pass  off  into  solution  as  pos- 
itive ions.  For  example, 

Zn-2  electrons  -^  Zn++ 

*  For  fuller  discussion  and  references  see  Jones,  Elements  of  Physical  Chemistry, 
pp.  486-488. 


MIGRATION  OF  IONS  273 

Notice  that  this  process  is  also  the  reverse  of  that  taking  place  at  the 
cathode. 

We  may  mention  also  the  following  more  complicated  oxidations 
occurring  at  the  anode: 

If  sulphuric  acid  or  a  sulphate  is  electrolyzed,  864  is  not  given  off  at 
the  anode,  but  oxygen  instead.  SCU  exists  only  as  an  ion,  never  in 
neutral  molecular  form.  According  to  the  old  theory,  the  reaction  by 
which  oxygen  is  formed  is  as  follows:  SO4~  ion  discharges  by  delivering 
up  its  electrons;  and  then,  not  being  capable  of  existing  in  the  neutral 
form,  it  reacts  with  water  to  regenerate  sulphuric  acid  and  at  the  same 
time  produce  oxygen  gas,  thus : 

2SO4+H2O  -*  H2SO4+O2 

According  to  the  new  theory,*  the  OH~  ions  coming  from  a  slight 
ionization  of  the  water  discharge  instead  of  the  SO4=,  and  then  react 
with  each  other  to  form  water  and  oxygen  gas,  thus : 

2OH-+2OH-  ->  2H2O+ O2 

Which  one  of  these  explanations  is  the  true  one  probably  depends,  as  in 
the  cathode  reaction,  upon  conditions  of  current  density.  If  the  current 
is  heavy  it  seems  inconceivable  that  the  extremely  small  amount  of 
OH~  ion  can  carry  it  alone.  With  weak  currents  it  may  do  so;  but  it 
must  be  remembered  that  the  concentration  of  the  OH~  is  constantly 
decreasing  on  account  of  the  accumulation  of  H+  ions. 

Whichever  is  the  true  explanation,  the  final  result  is  the  same; 
namely,  oxygen  is  evolved  and  the  ions  of  the  acid  accumulate  around 
the  anode. 

When  nitric  acid  or  a  nitrate  is  electrolyzed,  the  anode  reaction  is 
exactly  the  same  as  with  a  sulphate — oxygen  is  evolved,  and  the  ions  of 
nitric  acid  accumulate  around  the  anode.  The  explanation  is  the  same 
here  also. 

With  a  hydroxide,  like  NaOH,  we  also  obtain  oxygen  at  the  anode; 
and  in  this  case  there  is  only  one  thing  that  can  happen,  namely,  the 
discharge  of  OH~  and  the  subsequent  reaction  to  form  water  and 
oxygen,  f 

Migration  of  Ions. — We  have  already  noted  that  when  charged 
electrodes  are  placed  in  the  solution  of  an  electrolyte,  the  ions  are 
moved  towards  them,  the  negative  ions  towards  the  anode  and  the  pos- 

*  See  Jones,  loc.  dt. 

t  Unless  we  assume  that  OH  gives  a  slight  secondary  ionization  into  H+  and  O=, 
the  latter  being  discharged. 


274 


ELECTROCHEMISTRY 


itive  ions  towards  the  cathode.  We  wish  now  to  deal  with  the  relative 
and  absolute  speeds  with  which  ions  move,  and  to  show  how  such 
knowledge  may  be  of  use  to  us. 

The  matter  of  ionic  migration  was  studied  by  Hittorf,  long  before 
the  modern  theory  of  ionization  was  developed  (1853—1859).  The 
phenomena  he  discovered  led  him  to  believe  that  solutions  of  elec- 
trolytes contained  independent  ions  which  moved  at  different  rates  of 
speed.  Naturally,  scientists  paid  very  little  attention  to  these  radical 
notions  at  the  time,  and  it  was  only  in  the  light  of  our  modern  concep- 
tion of  ionization  that  their  importance  was  appreciated.  We  can  best 
understand  the  matter  by  studying  an  example — the  behavior  of  silver 
nitrate  in  solution: 

Suppose  we  have  this  solution  in  a  trough-like  cell  divided  by  two 
porous  partitions  into  three  compartments  (Fig.  40),  the  end  compart- 


fl 


FIG.  40. — Migration  of  Ions. 

ments  containing  silver  electrodes.  Suppose  also  that  the  solution  is  of 
such  concentration  that  the  anode  and  cathode  compartments  each 
contain  one  equivalent  of  electrolyte.  If  we  should  pass  96,500 
coulombs  of  electricity  through  the  solution,  one  equivalent  of  silver 
would  plate  out  on  the  cathode,  and  a  like  amount  would  enter  the  , 
solution  at  the  anode.  If  there  were  no  movement  of  the  ions,  we 
should  expect  the  cathode  compartment  to  have  lost  all  its  silver  ions 
and  the  anode  compartment  to  have  doubled  its  concentration.  In 
practice,  however,  this  does  not  happen.  We  do  notice  a  decrease 
in  the  concentration  of  silver  at  the  cathode,  but  not  so  great  a  decrease 
as  the  non-movement  of  the  ions  would  demand.  At  the  anode,  also, 
we  notice  an  increase  in  concentration,  but  it  is  not  so  great  as  we 
should  expect.  In  the  middle  compartment  we  should  expect  no 
change  in  concentration,  and  in  actual  practice  we  get  none. 

The  only  plausible  way  of  explaining  these  changes  in  concentration 
is  by  supposing  that  silver  ions  move  out  of  the  anode  compartment  and 
into  the  cathode  compartment.  If  we  investigate  the  concentration 
of  the  NOs=  ions,  we  have  to  suppose  a  movement  of  this  radical  in  the 
opposite  direction. 

Now,  as  to  the  relative  speeds  of  these  ions:  In  actual  practice  we 
find  that  when  96,500  coulombs  of  electricity  have  passed  through  the 


MIGRATION  OF  IONS  275 

above  solution,  the  anode  compartment  contains  1.527  equivalents  of 
silver  instead  of  2  equivalents.  Evidently  2  — 1.527,  or  0.473,  equivalent 
of  silver  must  have  moved  out  of  the  compartment.  Analysis  shows  also 
that  the  compartment  contains  an  amount  of  NOs"  ions  exactly  equiva- 
lent to  the  silver,  i.e.,  1.527  equivalents.  Now,  since  at  the  beginning 
there  was  only  1  equivalent  of  NOs~,  0.527  equivalent  must  have  moved 
into  the  compartment. 

In  the  cathode  compartment  we  find,  instead  of  no  silver  at  all, 
0.473  equivalent  (the  amount  which  left  the  anode  compartment),  and 
instead  of  1  equivalent  of  NOa^we  find  0.473  equivalent,  0.527  equivalent 
having  left  (the  amount  which  entered  the  anode  compartment). 

So  we  see  that  the  measurements  of  the  changes  in  concentration  at 
both  electrodes  lead  to  the  same  conclusion ;  namely,'  that  0.473  equiva- 
lent of  Ag+  have  moved  towards  the  cathode  and  0.527  equivalent  of 
NOa~  towards  the  anode.  This  means  that  the  relative  speeds  of  these 
two  ions  are:  Ag+  473,  NOa~  527;  and  since  all  the  current  is  carried 
by  the  ions  it  means  also  that  the  silver  ion  does  473/1000  of  the  con- 
ducting and  the  nitrate  ion  527/1000.  These  values  are,  however,  not 
entirely  independent  of  dilution;  and  at  high  temperatures  all  values 
approach  0.5,  indicating  equal  conductance  for  both  ions.* 

It  is  a  little  difficult  to  see  that  after  the  above  changes  the  silver  and 
nitrate  ions  still  balance  in  each  compartment.  This  can  be  cleared  up 
by  simply  balancing  accounts.  Take  the  anode  compartment,  stating 
the  values  in  equivalents : 

Ag+  at  start 1 

Ag+  from  anode 1 

Total 2 

Moved  out..  .    0.473 


Final    amount 1.527 

NO3-  at  start 1 

Moved  in .  .  .    0.527 


Final    amount 1.527 

It  may  be  shown  similarly  that  the  cathode  compartment  contains 
finally  0.473  equivalent  of  each  ion. 

Numbers  such  as  these  for  Ag+  and  NO3~  can  be  worked  out  for  all 

*  See  Bigelow,  Theoretical  and  Physical  Chemistry,  p.  447. 


276  ELECTROCHEMISTRY 

the  ions;  and  as  they  show  the  relative  part  taken  by  different  ions  in 
the  transportation  of  the  current,  they  are  called  ordinarily,  "  trans- 
port numbers."* 

If  it  is  desired  to  know  the  absolute  velocity  of  the  ions — i.e.,  the 
number  of  centimeters  over  which  they  move  in  one  second,  this  may 
be  accomplished  very  easily  in  many  cases  by  use  of  the  simple  U-tube 
apparatus.  Suppose,  for  example,  we  wish  to  know  the  rate  of  migra- 
tion of  H+  ion.  We  place  in  the  tube  a  dilute  solution  of  some  elec- 
trolyte, say  sodium  chloride,  thickened  and  kept  in  place  by  means  of 
gelatine  or  agar,  also  made  slightly  alkaline  and  colored  pink  with  a 
drop  of  phenolphthalein.  At  the  anode  end  of  the  tube  we  place  some 
dilute  acid.  We  first  allow  the  apparatus  to  stand  without  applying  a 
potential,  and  note  carefully  the  rate  at  which  the  H+  ion  diffuses  and 
decolorizes  the  indicator.  We  then  apply  a  certain  known  potential 
and  notice  a  much  more  rapid  movement  of  the  H+  ion.  The  differ- 
ence between  the  two  rates  of  movement  is  the  rate  of  migration  we 
are  seeking. 

Rates  of  migration  are  usually  stated  in  centimeters  per  second  under 
a  potential  gradient  of  1  volt  per  centimeter.  If  the  tube  used  is  40  cm. 
long  and  a  potential  of  40  volts  is  applied,  the  fall  or  "  gradient  "  is 
1  volt  per  centimeter.  Hydrogen  ion  moves  the  most  rapidly  of  all 
ions,  but  its  velocity  under  a  potential  gradient  of  1  volt  per  centi- 
meter is  only  0.0032  cm.  per  second  at  18°  C.  Hydroxyl  ion  comes 
next  to  hydrogen,  with  a  velocity  of  0.0018  cm.  per  second. 

A  practical  application  of  this  principle  of  ionic  migration  is  found  in 
the  study  of  complex  ions.  If  it  is  suspected  that  a  certain  complex 
exists,  the  solution  supposed  to  contain  it  is  treated  according  to  one  of 
the  methods  described  above,  it  is  usually  possible  to  tell,  by  the  direc- 
tion and  amount  of  movement  of  certain  elements,  whether  the  given 
complex  exists  or  not.  Thus  concentrated  solutions  of  cupric  bromide 
were  suspected  of  containing  the  anion  CuBrs".  The  color  of  such  a 
solution  is  brown,  and  when  it  was  treated  as  above  the  boundary  line  of 
the  brown  moved  towards  the  anode  while  blue  copper  ions  moved 
towards  the  cathode.  Moreover,  more  copper  moved  out  of  the  cathode 
compartment  than  into  it,  which  was  to  be  expected  if  the  complex  salt 
involved  was  Cu(CuBr3)2,  for  the  anion  carries  twice  as  much  copper  as 
the  cation.  The  presence  of  the  complex  anion  was  finally  proved  by  a 
quantitative  study  of  these  transport  relations,  f 

Conductivity. — We  have  already  defined  conductivity  as  the  recip- 
rocal of  resistance,  i.e.,  where  resistance  is  stated  in  ohms,  conductivity  is 

*  Also  called  "  transference  numbers." 

t  Denham,  Zeitschr.  physikal.  Chemie,  66,  641  (1909). 


CONDUCTIVITY  AND   DILUTION  277 

stated  in  reciprocal  ohms,  or  mohs.  Specific  conductivity  we  have 
defined  as  the  conductivity  of  a  centimeter  cube  of  a  substance  or  solu- 
tion. In  practice  the  term  "  specific  "  is  usually  omitted,  but  when  we 
speak  of  the  "  conductivity  "  of  a  solution  the  term  "  specific  "  is  always 
understood. 

Conductivity  is  usually  designated  by  the  Greek  letter  *,*  and  to 
denote  the  dilution  of  the  solution  we  write  below  this  symbol  the  number 
of  liters  containing  1  mole  of  solute.  Thus  ^32  means  the  (specific) 
conductivity  of  a  solution  at  a  dilution  of  32  liters,  i.e.,  where  1  mole  is 
contained  in  32  liters. 

Molecular  conductivity  is  the  total  conductivity  of  a  solution  con- 
taining 1  mole  of  solute,  as  it  would  be  if  the  solution  were  placed 
between  two  flat  electrodes  of  indefinite  size  and  one  centimeter  apart. 
Its  value  is  obtained  by  multiplying  the  (specific)  conductivity  by  the 
number  of  cubic  centimeters  required  to  include  1  mole  of  solute  at 
the  given  dilution.  Thus,  if  ^32  for  a  given  solution  is  0.0027  the 
molecular  conductivity  is,  0.0027X32,000  or  86.4.  Molecular  con- 
ductivity is  designated  by  the  Greek  letter  /*.  f 

Conductivity  and  Dilution. — Specific  conductivity  decreases  with 
dilution.  We  should  expect  this,  for  the  more  dilute  a  solution  is  made, 
the  greater  is  its  resistance.  But  the  decrease  in  conductivity  is  not  so 
great  as  the  dilution  alone  would  tend  to  make  it.  If  dilution  meant 
nothing  more  than  a  lowering  of  concentration,  K\Q  would  invariably  be 
half  of  KB;  that  is,  at  10  liters  dilution  there  would  be  half  as  many  ions 
per  cubic  centimeter  to  conduct  the  current,  and  therefore  the  con- 
ductivity would  be  half  as  great.  But  the  conductivity  at  10  liters  is 
always  more  than  half  as  great  as  at  5  liters,  and  this  we  account  for 
by  supposing  that  in  the  process  of  dilution  more  ions  are  produced  by 
dissociation  of  previously  undissociated  molecules. 

Molecular  conductivity  increases  with  dilution  up  to  a  certain  max- 
imum value.  This  again  is  what  we  should  expect,  for  molecular  con- 
ductivity is  the  conductivity  of  a  whole  mole  or  solute,  due,  of  course,  to 
the  ions  alone,  and  the  more  dilute  the  solution  the  greater  is  the  per- 
centage of  ionization;  but  when  the  dilution  is  sufficient  to  produce  com- 
plete ionization  further  dilution  would  produce  no  effect.  The  maximum 
molecular  conductivity  of  a  solution  is  called  the  molecular  conductivity 
at  "  infinite  dilution,"  and  is  designated  by  Moo-t 

The    following    table    shows   the  values    of  /.'-,    for    several    elec- 

*  Pronounce  "  kappa." 

t  Pronounce  "  mew." 

t  Read  "  mew  sub  infinity." 


278 


ELECTROCHEMISTRY 


trolytes  at  different  dilutions.     The  manner  in  which  the  values  approach 
a  maximum  can  be  seen : 


Ml 

M10 

M100 

M1000 

M10>000 

KC1  
NaCl          .  . 

98 
74 

112 
92 

122 
101 

127 
106 

129 
108 

AgNO3  

68 

94 

108 

113 

115 

HC1  

301 

351 

370 

377 

377 

KOH 

184 

213 

228 

234 

243 

CuSO4 

51 

87 

143 

197 

220 

HC2H3O2  

1.32 

4.67 

14.5 

41 

107 

Note  that  HC1  and  KOH  reach  their  maximum  value,  /x^,  at  a 
dilution  of  1000  liters.  Note  also  that  the  first  three  salts,  KC1,  NaCl 
and  AgNOs,  have  nearly  reached  their  maximum  at  10,000  liters, 
but  that  the  value  for  CuSCU  is  still  rapidly  increasing  at  this  dilution. 
Note  particularly  the  values  for  acetic  acid. 

Degree  of  lonization  from  Conductivity. — If  conductivity  is  due  to 
the  ions  alone  and  if  maximum  molecular  conductivity  means  complete 
ionization,  then  by  comparison  of  the  value  for  a  given  dilution  with  the 
maximum  value  we  should  be  able  to  calculate  the  degree  of  ionization 
of  an  electrolyte  at  this  dilution.  Thus,  if  the  value  of  /*,  at  any  given 
dilution,  is  one-half  the  value  of  nx,  we  reason  that  the  substance  is  50 
per  cent  ionized  at  this  dilution.  The  value  of  ^  for  HC1  is  377  and  juio 
is  351.  The  degree  of  ionization  at  10  liters  is  351/377  or  90.3  per  cent. 
Remember  that  the  conductivity  values  give  us  absolutely  no  clue  as  to 
the  degree  of  ionization  unless  we  know  the  value  of  /^  for  the  given 
electrolyte.  Thus,  we  cannot  reason  that  NaCl  is  less  highly  ionized 
than  KC1  at  10  liters  simply  because  the  conductivity  is  less. 

Conductivities  of  the  Single  Ions. — By  combining  the  transport 
numbers  and  the  values  of  /^  we  are  able  to  calculate  the  total  conduc- 
tivity, at  complete  dissociation,  of  a  single  ion.  We  can  thus  construct  a 
table  of  values  of  fj.x  for  all  the  ions,  and  from  this  we  can  predict  what 
will  be  the  value  of  /^  for  any  substance  made  up  by  combining  these 
ions.  In  some  cases  this  possibility  is  of  great  use,  for  there  are  cases — 
notably  the  weak  electrolytes  like  acetic  acid — where  the  value  of  ju^ 
cannot  be  determined  directly.  Note  the  following  examples : 

According  to  the  conductivity  table  above  the  value  of  M^  for  HC1  is 
377.  The  transport  number  for  H+  is  0.828  and  for  Cl~  0.172;  and 
since  each  of  these  ions  carries  the  same  charge,  this  means  that  828/1000 


DEGREE  OF  IONIZATION  FROM   CONDUCTIVITY 


279 


of  the  current  is  carried  by  the  hydrogen  ion,  and  172/1000  by  the  chlor- 
ide ion.  The  conductivity,  therefore,  due  to  the  H+  ion,  is  828/1000 
of  377,  or  312,  and  that  due  to  the  Cl~  ion,  is  172/1000  of  377,  or  65. 
By  a  similar  method  we  should  find  that  the  value  for  Na+  was  44; 
for  OH~,  174;  and  for  acetate  ion,  C2HsO2~,  35,  etc. 

The  table  below  gives  the  values  of  ^  for  a  number  of  common  ions: 

MOLECULAR   CONDUCTIVITIES  OF  SINGLE  IONS  AT  INFINITE 

DILUTION  * 


Ions. 

Moo 

Ions. 

Moo 

Ions. 

Moo 

Li+                    

33.44 

Mg++ 

92.0 

Cl- 

65.4 

Na+ 

43  55 

Zn+  + 

93.4 

I- 

66.4 

K+  
Rb+                       .... 

64.67 
67.6 

Cu+  + 
Cd+  + 

94.6 
95.0 

Br~ 
C2H3O2- 

67.6 
35.0 

Cs+ 

68  2 

Ca+  + 

103.6 

C2O4= 

122.0 

NH4+  

Ag+ 

64.4 
54.0 

Ba+  + 
Pb+  + 

111.0 
122.6 

S04= 
CO3= 

136.8 
140  (?) 

H+ 

312  0 

HCT+  + 

96.0 

C1O3~ 

55 

Co+  + 

Ni+  + 

91.0 
90.0 

NO3~ 
OH- 

61.8 
174.0 

*  Taken  from  various  sources,  but  largely  calculated  from  data  in  Landoldt- 
Bornstein-Roth,  "  Physikalisch-Chemisch  Tabellen,"  fourth  edition. 

The  values  given  in  this  table  will  be  found  very  useful,  as  men- 
tioned above.  For  example,  we  often  want  to  know  the  degree  of  ioniza- 
tion  of  some  salt  or  acid,  and  in  the  tables  of  constants,  such  as  Landoldt- 
Bornstein,  can  only  find  the  conductivity  for  the  given  concentration. 
We  must,  of  course,  know  the  value  of  ^  for  the  given  case  before  we 
can  calculate  our  degree  of  ionization,  and  we  can  always  get  this  from  a 
table  such  as  the  above  if  it  is  only  complete  enough,  and  this  by  the 
simple  process  of  adding  together  the  conductivities  of  the  separate  ions. 
Thus,  perhaps  we  want  to  know  the  degree  of  ionization  of  M/10 
Cu(NOs)2.  We  look  up  the  conductivity  data  in  Landoldt-Bornstein 
(p.  1107)  where  we  find  that  the  equivalent  conductivity  at  this  con- 
centration is  82.4.  Since  the  mole  of  this  salt  contains  two  equivalents, 
the  molecular  conductivity,  mo,  should  be  2X82.4,  or  164.8.  From  the 
table  above  we  find  the  value  of  MOO  to  be  94-6  +  (2  X  61.8),  or  217.2. 
We  can  now  find  the  degree  of  ionization  in  the  usual  way.  The  value 
is  164.8/217.2,  or  75.8  per  cent. 

In  some  cases  the  use  of  such  values  as  the  above  gives  us  the  only 
method  we  have  of  determining  a  value  of  ^.  Suppose,  for  example, 


280  ELECTROCHEMISTRY 

we  want  this  value  for  acetic  acid.  We  cannot  determine  it  directly 
by  successively  diluting  the  solution  until  we  obtain  the  maximum 
conductivity,  for  before  the  limiting  value  is  reached  the  solution  must 
be  made  so  dilute  that  the  errors  of  observation  render  the  results 
valueless.  What  we  must  do  is  to  add  together  the  limiting  values 
for  hydrogen  ion  and  acetate  ion  as  seen  in  the  above  table.  The  value 
thus  obtained  is  347  (312+35). 

Chemical  Electromotive  Force. — When  a  metal  is  placed  in  contact 
with  a  solution  of  one  of  its  salts,  the  metallic  atoms  tend  to  go  into 
solution  and  become  metallic  ions,  and  this  tendency  is  opposed  by  the 
osmotic  pressure  of  the  ions,  which  would  cause  them  to  return  to  the 
metallic  condition.  But,  to  become  metallic  ions,  the  atoms  of  the 
metal  must  leave  behind  them  negative  charges  on  the  electrode,  and  to 
become  metallic  atoms  the  ions  must  take  on  negative  charges  from  the 
electrodes.  What  will  actually  happen,  then,  is  this:  If  the  osmotic 
pressure  of  the  ions  is  greater  than  the  solution  pressure  of  the  metallic 
atoms  a  few  ions  will  discharge  by  taking  on  electrons  from  the  metal. 
This  will  leave  the  metal  electro-positive,  and  the  ions  will  then  be 
repelled  and  the  action  will  cease.  If  the  solution  pressure  is  greater 
than  the  osmotic  pressure  of  the  ions,  a  few  metallic  atoms  will  pass  into 
ions  by  giving  up  electrons  to  the  metal.  This  will  make  the  metal 
electrically  negative,  and  further  giving  up  of  positive  ions  will  be  pre- 
vented.* It  is  to  be  understood,  of  course,  that  the  amount  of  metal 
dissolved  or  plated  out  by  this  process  is  too  small  to  be  measured,  unless, 
as  we  shall  see  later,  we  can  find  some  way  of  drawing  off  the  opposing 
charge  left  on  the  metal,  and  thus  allowing  the  action  to  continue. 

Where  the  osmotic  pressure  is  greater  than  the  solution  pressure  it 
is  balanced  by  the  solution  pressure  and  the  electrical  potential  which  is 
developed,  thus: 

os.  pr.  =sol.  pr.+E.M.F. 

Where  the  solution  pressure  is  the  greater,  it  is  balanced  by  the  osmotic 
pressure  and  the  potential,  thus: 

sol.  pr.  =os.  pr.+E.M.F. 

An  inspection  of  these 'two  equations  shows  at  once  that  the  E.M.F. 
represents  the  difference  between  the  solution  pressure  and  the  osmotic 
pressure,  expressed  in  volts. 

If  we  prepare  a  series  of  salt  solutions  having  the  same  ionic  osmotic 

*  This  "  double  layer  "  theory  of  potential  was  first  developed  by  Nernst,  Zeitschr. 
physikal.  Chemie,  4,  129. 


CHEMICAL  ELECTROMOTIVE  FORCE  281 

pressure  and  place  in  each  a  rod  of  the  corresponding  metal,  we  find,  by 
making  the  proper  measurements,  that  the  potentials  developed  in  the 
several  cases  differ  widely.  This,  we  note  at  once,  must  be  due  to  dif- 
ferences in  solution  pressure.  Metals  like  magnesium  and  zinc  will 
show  a  high  potential,  developed  in  such  a  direction  that  it  would 
cause  a  current  to  flow  from  the  metal  to  the  solution  if  the  proper  con- 
ditions were  presented.  We  know,  therefore,  that  the  solution  pressure 
of  these  metals  greatly  exceeds  the  osmotic  pressure  of  their  normal  ion, 
and  from  their  ability  to  do  work  of  a  positive  kind,  due  to  this  high 
solution  pressure  and  their  positive  nature,  we  call  them  intensely  elec- 
tro-positive. The  E.M.F.  also  developed  between  them  and  the  solu- 
tion we  call  positive.  Figuratively  speaking,  such  metals  are  "  able  to 
wind  up  the  weight."  They  have  an  intense  desire  to  go  into,  and 
remain  in,  the  ionic  condition.  They  are  the  metals  which  in  nature 
are  never  found  free,  but  always  in  the  condition  of  some  compound. 

On  the  other  hand,  we  find  metals  like  silver  and  gold  which  in 
contact  with  their  normal  ion  allow  the  development  of  considerable 
potential,  but  of  the  opposite  kind  from  that  above.  This  potential 
would  cause  a  current  to  flow  from  the  solution  to  the  metal.  We  know, 
therefore,  that  in  these  cases,  the  osmotic  pressure  greatly  exceeds  the 
solution  pressure.  We  cannot  call  them  electro-negative  because  they 
form  positive  ions,  but  we  call  them  weakly  electro-positive;  and,  due 
to  the  fact  that  they  are  negatively  responsible  for  the  E.M.F.  developed 
between  them  and  the  solution,  we  give  this  E.M.F.  a  negative  sign. 
These  metals  are  always  willing  to  go  out  of  the  ionic  condition  if  they 
are  given  any  encouragement.  They  are  the  metals  which  in  nature 
are  found  free  and  uncombined. 

Between  the  two  extremes  we  have  described,  we  find  varying 
degrees  of  positiveness,  from  those  which  are  much  like  magnesium 
to  those  which  are  much  like  gold;  and  again  we  find  those  which,  in 
contact  with  their  normal  ion,  show  almost  no  E.M.F.  This  does  not 
mean  that  these  metals  are  electrically  neutral,  but  that  their  solution 
pressure  almost  equals  the  osmotic  pressure  of  the  ion. 

What  has  been  said  about  the  metals  may  also  be  said  about  negative 
substances  like  chlorine  and  sulphur.  These  substances  have  in  general 
rather  high  solution  pressures;  but  since  they  always  form  negative  ions 
they  invariably  leave  a  positive  charge  on  the  electrode.  In  this  these 
substances  are  something  like  gold.  The  only  difference  is  that  in  one 
case  the  osmotic  pressure  more  than  balances  the  weak  solution  pressure 
of  a  positive  element  to  develop  a  negative  E.M.F.,  while  in  the  other 
the  solution  pressure  of  a  negative  element  exceeds  the  osmotic  pressure 
to  do  the  same  thing.  These  elements  are  anxious  to  do  work,  but  the 


282 


ELECTROCHEMISTRY 


only  work  they  can  do  is  of  a  negative  kind.     They  "  dig  a  pit  for  the 
the  weight  to  drop  into." 

POTENTIAL  SERIES 


Element/Normal 

Absolute  Standard  : 

Hydrogen  Standard: 

Ion. 

Sign  of  Solution. 

Sign  of  Electrode. 

K/K+ 

+  (2.93) 

-(3.20) 

Na/Na+ 

+  (2.55) 

-(2.82) 

Ba/Ba+  + 

+(2.55) 

-(2.82) 

Sr/Sr+  + 

+(2.50) 

-(2.77) 

Ca/Ca+  + 

+(2.29) 

-(2.56) 

Mg/Mg+  + 

+2.27 

-2.54 

A1/A1+++ 

+1.01 

-1.28 

Mn/Mn+  + 

+0.80 

-1.07 

Zn/Zn++ 

+0.50 

-0.77 

Cd/Cd++ 

+0.15 

-0.42 

Fe/Fe+  + 

+0.07 

-0.34 

CO/GO+  + 

-0.04 

-0.23 

Ni/Ni++ 

-0.05 

-0.22 

Sn/Sn+  + 

-0.08 

-0.19 

Pb/Pb+  + 

-0.12 

-0.15 

H2/H+ 

-0.27 

±0.00 

CU/GU++ 

-0.60 

+0.33 

AS/AS+++ 

-0.60(?) 

+0.34 

Bi/Bi+++ 

-0.66 

+0.39 

Sb/Sb+++ 

-0.73 

+0.46 

Hg/Hg+ 

-    .02 

+0.75 

Ag/Ag+ 

-    .04 

+0.77 

Pt/Pt++++ 

-    .13 

+0.86 

AU/AU+++ 

-    .35 

+  1.08 

F2/F- 

-    .23 

+  1.96 

cyci- 

-    .69 

+  1.42 

Br2/Br~ 

-    .26 

+0.99 

VI- 

-0.79 

+0.52 

02/OH~ 

-0.70 

+0.43 

We  cannot  describe  here  the  methods  used  in  determining  the  poten- 
tials developed  between  a  metal  and  its  solution;  but  we  may  say  that 
two  types  of  values  are  in  use.  The  first  is  supposed  to  represent 
exactly  what,  from  the  above  discussion,  we  should  expect  to  get.  That 
is,  the  values  are  supposed  to  represent  the  actual  potentials  developed 
between  the  metals  and  their  ion,  and  we  should  expect  elements  like 
magnesium  and  zinc  to  be  listed  with  a  positive  E.M.F.  and  elements  like 


ELECTROMOTIVE  FORCE  AND  CONCENTRATION  283 

gold  with  a  negative  E.M.F.  Since,  as  we  have  stated,  positive  ions  go 
into  solution  to  give  a  positive  E.M.F.  and  out  of  solution  to  give  a 
negative  E.M.F.,  the  sign  we  should  use  is  really  the  sign  of  the  charge 
developed  in  the  solution.  In  the  other  set  of  values  the  E.M.F.  for 
hydrogen  is  arbitrarily  made  zero,  and  the  other  values  are  related  to 
this  as  in  the  first  table.  The  sign  also  is  the  reverse  of  that  used  in  the 
first  set  of  values,  namely  the  sign  of  the  metal.  The  table  on  page  282 
gives  the  two  sets  of  values.  It  is  understood  in  each  case  that  the  con- 
centration of  the  ion  is  normal.  The  values  are  given  in  volts. 

In  addition  to  the  difference  in  sign,  it  will  be  noted  that  the  zero 
point  of  the  scale  at  the  right  is  0.27  volt  farther  down.  Therefore,  to 
translate  values  from  the  first  series  to  those  of  second,  add  0.27  alge- 
braically, and  then  change  the  sign.  Thus,  for  Hg+  we  have  —1.02 
+0.27  =  -0.75,  changing  then  to  +0.75;  for  Mn++,  +0.80+0.27  = 
+  1.07,  changing  to  -1.07. 

Electromotive  Force  and  Concentration. — The  values  in  the  above 
table  hold  only  for  normal  ion  concentration.  For  any  other  concen- 
tration the  values  will  be  somewrhat  different,  as  we  shall  now  show. 
We  have  shown  that  the  potential  developed  between  a  metal  and  its 
solution  is  measured  by  the  difference  between  the  osmotic  pressure  of 
the  ion  and  the  solution  pressure  of  the  metal,  and  under  the  absolute 
standard  have  given  the  values  for  the  potentials  positive  signs  where 
the  solution  pressure  preponderated.  Evidently,  then,  these  values 
would  be  decreased  (algebraically)  by  increasing  the  concentration  of  the 
ion,  and  increased  (algebraically)  by  decreasing  the  concentration. 

The  actual  value  of  this  increase  or  decrease  in  potential  involves  the 
following  considerations:  Univalent  ion  of  normal  concentration  gives 
an  osmotic  pressure  of  22.4  atmospheres.*  Bivalent  ion  of  normal 
concentration  contains  half  as  many  particles  per  cubic  centimeter  and 
therefore  gives  an  osmotic  pressure  of  1 1 .2  atmospheres.  In  other  words, 
the  change  in  osmotic  pressure  due  to  addition  of  an  ion  is  inversely 
proportional  to  the  valence,  which  may  be  indicated  as  1/n.  The  solu- 
tion pressure  of  a  metal  remains  constant,  so  that  any  change  in  poten- 
tial is  due  entirely  to  change  in  osmotic  pressure;  and  it  has  been  found 
that  a  ten-fold  change  in  osmotic  pressure  gives  a  change  of  0.058  volt 
in  the  potential.  Now,  every  time  we  have  a  ten-fold  change  in  the  con- 
centration of  a  univalent  ion  we  have  a  ten-fold  change  in  osmotic 
pressure,  and  must  therefore  change  the  potential  by  0.058  volt.  For  a 
bivalent  ion  a  ten-fold  change  in  concentration  will  give  only  half  as 
much  change  in  osmotic  pressure  and  so  will  change  the  potential  by 
only  0.058/2  volt.  In  general,  then,  the  change  in  potential  is  pro- 
*  Same  as  that  of  a  non-ionized  substance  of  molar  concentration. 


284  ELECTROCHEMISTRY 

portional  to  the  logarithm  of  the  change  in  concentration  and  to 
0.058/n,  that  is,  to 

0.058        1 

(1)  -  log  - 

n  c 

where  1  is  a  concentration  of  1  normal  and  c  the  new  concentration. 

We  have  noted  that  increasing  the  concentration  (algebraically) 
decreases  the  potential,  and  that  decreasing  the  concentration 
increases  the  potential.  In  line  with  this,  we  notice  that  where  c  is 
greater  than  1,  log  1/c  will  have  a  minus  sign,  making  expression  (1) 
negative  as  a  whole.  Where  c  is  less  than  1,  the  opposite  is  true. 
Therefore,  if  we  let  P  stand  for  the  final  potential  and  PN  for  the  normal 
value,  the  following  relationship  holds  for  all  concentrations: 

.  0.058  .      1 
P  =  P»+—  log- 

As  an  example,  let  us  work  out  the  potential  between  copper  and  0.001 
N  copper  ion.  PN  =  —0,6,  n=2,  and  c  =0.001.  Substituting  values, 
we  have 

i          ! 

log 


log  7=3;  therefore  P=  -0.6+(0.029X3)  or  -0.513. 
U.UUl 

A  Primary  Cell.  —  We  have  seen  that  when  a  metal  dissolves,  it  must 
go  into  the  ionic  condition;  and  to  do  this  in  contact  with  a  solution  of 
one  of  its  own  salts,  it  must  leave  behind  it  a  negative  charge.  We 
have  seen  also  that,  to  plate  out  of  its  own  solution,  a  metal  must  take 
on  a  negative  charge.  Again,  we  have  noted  that  the  process  in  either 
case  is  instantly  stopped  by  the  potential  developed,  unless  some  means 
is  found  of  drawing  off  the  electric  charges.  Finally,  we  have  rioted 
that  some  metals  in  contact  with  their  salt  solutions  develop  a  strong 
positive  E.M.F.,  and  therefore  have  a  high  solution  pressure,  while 
other  metals  allow  the  development  of  a  negative  E.M.F.,  and  there- 
fore have  a  low  solution  pressure.  We  have  now  to  consider  methods  of 
drawing  off  and  utilizing  the  charges  developed  as  above,  and  also 
methods  of  regulating  their  intensity  —  in  other  words,  the  theory  of  the 
primary  cell. 

In  a  cell  of  the  Daniell,  or  "  gravity,"  type  we  have  two  metals  of 
widely  different  potential,  each  dipping  into  a  solution  of  one  of  its  own 
salts.  Thus,  in  the  Daniell  cell  we  have  zinc  dipping  into  zinc  sulphate 
solution  and  copper  dipping  into  copper  sulphate  solution,  the  two  solu- 
tions being  in  contact  but  prevented  from  mixing  by  means  of  a  porous 


A  PRIMARY  CELL 


285 


partition.  In  the  gravity  cell  we  have  the  same  solutions  and  the  same 
metals,  but  the  copper  solution  is  kept  from  mixing  with  the  zinc  solu- 
tion simply  by  making  it  more  concentrated  and  heavy  and  placing 
it  underneath.  Fig.  41  will  serve  to  indicate  the  relative  positions  of 
the  several  components  of  either  of  these  cells. 

If  we  use  solutions  containing  normal  ion  concentration  of  each 
electrolyte,  there  will  be  developed  between  the  zinc  and  its  solution 
a  positive  E.M.F.  of  0.5  volt,  tending  to  drive  the  current  into  the 
solution,  and  between  the  copper  and  its  solution  a  negative  E.M.F.  of 
0.6  volt,  tending  to  draw  the  current  out  of  the  solution.  Note  that 
these  two  tendencies  act  in  the  same  direction,  and  that  their  sum  is 


Zn 

c 

: 

^             ZnSO4 

CuSO4 

FIG.  41. — Diagram  of  the  Daniell  Cell. 

1.1  volts.*  When,  therefore,  the  two  electrodes  are  connected  by  means 
of  a  wire,  a  current  flows  through  the  wire  from  the  copper  to  the  zinc 
under  a  head  of  1.1  volts.  Zinc  goes  into  solution  to  form  zinc. ion, 
copper  ion  goes  out  of  solution  as  metallic  copper,  and  since  the  charges 
thus  developed  are  constantly  led  away  through  the  wire  the  process 
becomes  continuous,  and  will  remain  so  as  long  as  there  is  any  zinc  to 
dissolve  and  any  copper  to  plate  out. 

It  will  be  noted  that  if  this  process  is  allowed  to  continue  the  zinc 
solution  will  become  more  concentrated  and  the  copper  solution  more 
dilute.  Increase  in  the  concentration  of  the  zinc  ion  will  oppose  the 
passage  of  more  zinc  ions  into  solution,  and  depletion  of  copper  ion  will 
oppose  the  further  plating  out  of  copper.  Both  these  effects  will,  there- 
fore, lower  the  efficiency  of  the  cell.  To  make  the  cell  as  efficient  as 
possible,  then,  we  start  with  the  zinc  solution  very  dilute  so  as  to  allow 
for  increase  and  we  keep  the  copper  solution  concentrated  by  having 
present  solid  copper  sulphate,  which  will  dissolve  as  needed. 

This  effect,  due  to  change  in  concentration,  is  extremely  important 
and  should  be  well  understood.  If  the  zinc  ion  concentration  could 
become  so  great  that  its  osmotic  pressure  would  equal  the  solution 

*  A  more  accurate  statement  would  be  that  it  is  the  algebraic  difference  between 
+0.5  and  -0.6.  thus  +0.5  -(-0.6)  = +1. 1. 


286  ELECTROCHEMISTRY 

pressure  of  the  zinc,  no  potential  whatever  would  then  exist  between 
this  metal  and  its  solution.  This  condition  cannot  be  reached  because  a 
zinc  solution  of  such  enormous  concentration  cannot  exist;  but  the  con- 
dition is  approached  whenever  the  concentration  is  allowed  to  increase. 
A  ten-fold  increase  in  concentration  of  zinc  ion  decreases  the  electrode 
potential  0.02&  volt.  A  similar  but  opposite  effect  is  seen  at  the  copper 
electrode.  The  potential  in  the  latter  case  is  due  to  excess  of  osmotic 
pressure  over  solution  pressure,  and  if  the  copper  ion  concentration  is 
made  so  slight  that  its  osmotic  pressure  only  equals  the  slight  solution 
pressure  of  the  copper,  no  potential  will  exist.  If  this  condition  is 
presented,  and  the  potential  at  the  zinc  electrode  is  still  +0.5,  the 
total  E.M.F.  of  the  cell  will  then  be  only  0.5  instead  of  1.1  as  above. 
By  also  bringing  the  zinc  ion  concentration  as  high  as  possible,  how- 
ever, we  shall  have  lowered  the  total  E.M.F.  of  the  cell  to  about  0.4. 
But  at  the  copper  electrode  we  can  do  much  more;  we  can  bring  the 
osmotic  pressure  of  the  ion  as  much  below  the  slight  solution  pressure 
of  the  copper  as  it  originally  was  above  it,  and  then  at  this  side  we  shall 
have  a  back  E.M.F.  of  0.6  volt — more  than  enough  to  overcome  the 
forward  E.M.F.  of  the  zinc.  We  shall  then  actually  have  our  cell 
reversed,  giving  a  slight  current  in  the  backward  direction.  It  is  evi- 
dent that  the  actual  value  of  the  potential  and  its  direction  can  be 
worked  out  by  use  of  the  equation  developed  in  the  last  section,  pro- 
vided only  that  we  know  the  concentrations  of  the  ions. 

As  can  be  seen  by  inspection  of  the  table  of  potential  series,  there 
are  many  possible  combinations  which  could  be  utilized  for  the  construc- 
tion of  a  primary  cell.  But  there  are  several  things  to  be  considered 
in  making  the  proper  selection.  One  is  the  cost  of  the  materials; 
another  is  solubility  of  the  salts;  a  third  is  the  stability  of  the  metal 
in  contact  with  water;  and  a  fourth  is  the  difference  in  potential  between 
the  two  metals.  One  simple  combination  which  we  might  mention  is 
the  well-known  zinc-platinum  couple,  which  might  better  be  called 
"  zinc-hydrogen  "  couple,  since  platinum  has  no  part  in  the  reaction. 
This  cell  consists  of  a  strip  of  zinc  and  a  strip  of  platinum  dipping  into 
dilute  sulphuric  acid.  Zinc  goes  into  solution  and  hydrogen  is  evolved 
on  the  platinum.  The  E.M.F.  is  about  0.8  volt.  (Explain  this.) 

The  Normal  Cadmium  Cell. — Potential  is  often  measured  by  com- 
parison with  a  standard  cell  giving  a  constant  and  perfectly  definite 
E.M.F.  Evidently  the  ordinary  Daniell  cell  could  not  be  used  for  this 
purpose  because  of  the  possibility  of  change  in  the  concentrations  of  the 
solutions  used  and  the  consequent  change  of  potential.  The  cell  most 
used  for  this  purpose  is  the  so-called  cadmium  cell,*  in  which  the  solu- 
*  Also  called  the  "  Weston  cell." 


A  CONCENTRATION  CELL  287 

tions  are  saturated  and  are  kept  so  by  contact  with  crystals  of  the  cor- 
responding salts.  Obviously  no  change  in  concentration  is  possible 
with  this  arrangement,  for  if  one  of  the  metals  should  go  into  solution 
it  could  only  increase  the  proportion  of  solid,  and  if  a  metal  were  plated 
out,  solid  would  dissolve  to  restore  the  concentration.  A  diagram 
of  the  Weston  cell  is  shown  in  Fig.  42.  The  necessary  details  of 
construction  are  as  follows :  Limb 
A  of  the  cell  contains  pure  mer- 
cury at  the  bottom,  connected 
through  the  glass  to  a  binding 
post  outside.  In  contact  with  this 
is  a  pasty  mixture  of  mercurous 
sulphate  and  its  solution.  Above 
this  and  extending  around  into  the  ng  cd 

other  limb  is  a  similar  mixture  of  FIG.  42. — The  Weston  Cell, 

cadmium  sulphate  and  its  solution. 

At  the  bottom  of   limb    B    is    a    button    of    cadmium   (or    cadmium 
amalgam)  connected  with  a  second  binding  post  outside. 

If  this  cell  is  properly  constructed  it  gives  a  constant  E.M.F.  of 
1.0183  volts  at  20°  C.,  unaltered  for  years.  Moreover,  rather  consider- 
able changes  in  temperature  do  not  greatly  alter  the  potential. 

It  is  understood,  of  course,  that  such  a  cell  is  not  intended  for  use  as  a 
source  of  current.  Its  only  value  lies  in  its  reliability  as  a  standard 
of  comparison. 

A  Concentration  Cell. — From  previous  considerations,  it  can  be 
seen  that  it  might  be  possible  to  construct  a  cell  having  the  same  metal 
and  the  same  solution  at  both  electrodes,  simply  making  the  solution 
more  dilute  at  one  side.  Such  a  cell  would  be  called  a  "  concentration 
cell."  The  arrangement  would  be  like  that  of  the  Daniell  or  "  gravity  " 
cell,  but  we  should  have  one  metal,  say  zinc,  and  one  solution,  say  zinc 
chloride,  at  both  sides.  With  such  an  arrangement  we  should  have  a 
counter  E.M.F.  developed  at  each  electrode,  and  if  the  two  solutions 
were  of  equal  concentration  these  would  exactly  neutralize  each  other, 
and  no  current  would  flow.  If,  however,  one  solution  were  made  very 
concentrated  and  the  other  very  dilute,  the  E.M.F.  would  be  greater  on 
one  side  than  on  the  other,  and  a  current  would  flow  if  the  proper  con- 
nections were  made.  The  E.M.F.  developed  by  such  means  could  be 
made  rather  large,  since,  as  mentioned  above,  a  ten-fold  difference  in 
concentration  means  (for  zinc  ion)  0.029  volt,  and  the  difference  could 
be  made  as  great  as  desired.  The  current  that  could  be  drawn  from  such 
a  combination  would,  however,  always  be  small,  because  the  necessary 
dilution  of  one  of  the  solutions  would  make  the  internal  resistance  of  the 


288  ELECTROCHEMISTRY 

cell  very  large.  The  cell  does,  nevertheless,  have  some  important  uses, 
which  we  need  not  mention  here. 

In  the  case  of  concentration  cells  also,  the  potential  can  be  calcu- 
lated from  the  difference  in  concentration  and  the  valence  of  the  ion  by 
use  of  the  fundamental  equation.  It  must  be  noted,  however,  that  the 
value  of  PN  here  drops  out.* 

The  Drop  Electrode  and  Calomel  Electrode  and  the  Measurement 
of  Single  Potentials. — In  discussing  the  table  of  potential  series  we 
might  have  said  that  the  existence  of  two  sets  of  values  is  due  to  the  fact 
that  some  uncertainty  exists  as  to  the  matter  of  an  absolute  standard. 
It  is  impossible  to  determine  the  potential  developed  between  a  metal 
and  its  solution  by  simply  dipping  the  metal  into  the  solution  and 
then  connecting  with  a  voltmeter.  To  do  this  we  should  have  to 
connect  one  side  of  the  voltmeter  with  the  metal  and  the  other 
with  the  solution.  We  should  then  have  two  metals  in  the  solution, 
and  should  obtain  the  resultant  of  two  potentials,  as  in  the  Daniell  cell. 
In  obtaining  the  single  potentials,  then,  we  cannot  avoid  the  double  or 
"  couple  "  arrangement;  and  if  we  are  to  find  the  absolute  potentials 
developed  between  the  metals  and  their  solutions  we  must  have  on  one 
side  an  arrangement  which  will  give  zero  potential.  The  total  potential 
developed  by  the  couple  will  then  be  a  measure  of  the  potential  developed 
on  the  active  side  only.  The  so-called  "  dropping  electrode  "  of  mercury 
is  supposed  to  be  such  an  arrangement.  Mercury  is  allowed  to  flow 
from  a  fine  tip  down  through  a  mercurous  ion  solution.  As  it  issues  from 
the  tip  it  breaks  up  into  fine  droplets  which  are  supposed  to  carry  off  the 
charge  developed  and  thus  maintain  zero  potential  between  the  metal 
and  the  solution.  If,  then,  a  cell  were  constructed  as  shown  diagram- 
matically  for  the  Daniell  cell,  using  a  drop  electrode  in  one  compartment 
and  the  metal  whose  potential  is  to  be  determined  in  the  other,  the  total 
potential  developed  would  supposedly  be  the  potential  sought.  This 
was  the  method  by  which  the  so-called  "  absolute  "  values  given  in  the 
table  were  determined. 

But  the  drop  electrode  involves  difficult  manipulation,!  and  is  now 
scarcely  at  all  used  in  the  determination  of  single  potentials.  Instead 
we  use  the  so-called  "  calomel  electrode,"  which  consists  essentially  of 
mercury  in  contact  with  a  saturated  solution  of  mercurous  chloride 
(calomel).  The  common  arrangement  is  seen  in  Fig.  43.  At  the 
bottom  of  the  container  is  a  layer  of  mercury,  A .  Above  this  is  a  mix- 

*  W.  K.  Lewis  (Zeit.  phys.  Chem.,  63,  174)  has  tested  certain  concentration  cells 
and  finds  the  E.M.F.  in  accord  with  the  calculated  values. 

t  The  question  of  reliability  is  also  involved:  see  Le  Blanc,  Electrochemistry, 
pp.  239-243. 


THE  HYDROGEN  ELECTRODE 


289 


FIG. 


43.— The  Calomel 
Electrode. 


ture  of  calomel  and  mercury,  B.  The  rest  of  the  apparatus,  including 
the  tube  E,  is  filled  with  a  normal  solution  of  potassium  chloride  whose 
purpose  is  to  make  the  mixture  conducting.  Electrical  connection  is 
obtained  through  the  wire  D,  which  passes 
through  the  bottom  of  the  vertical  tube  into 
the  mercury,  and  through  the  tube  E  which 
connects  with  the  solution. 

The  calomel  electrode  does  not  give  zero 
potential,  but  its  actual  potential  has  been 
determined  once  for  all  by  means  of  the  drop 
electrode  and  has  been  found  to  be  —0.56  volt. 

In  using  this  electrode  for  the  determina- 
tion of  single  potentials,  the  tube  E  is  dipped 
into  the  solution  containing  the  other  elec- 
trode, and  the  total  potential  of  the  couple  is 
then  measured  by  comparison  with  a  standard 
cell.  The  unknown  single  potential  may  then 
be  calculated  by  difference. 

The  Hydrogen  Electrode  and  Measurement 
of  Hydrogen  Ion  Concentration. — A  strip  of 
platinum  covered  over  electrolytically  with 
platinum  black  adsorbs  on  its  surface  a  considerable  quantity  of  hydro- 
gen gas.  If  we  partly  immerse  such  a  strip  in  a  solution  containing 
hydrogen  ion  and  keep  the  upper  part  saturated  with  hydrogen  by 
passing  the  gas  over  it,  there  will  be  developed  the  same  conditions 
of  equilibrium  between  molecular  hydrogen  and  hydrogen  ion  as  we 
have  between  metallic  copper  and  copper  ion.  In  other  words  we 
have,  to  all  intents  and  purposes,  a  hydrogen  electrode. 

The  hydrogen  electrode  obeys  the  same  laws  with  regard  to  concen- 
tration as  do  other  electrodes.  Thus  with  normal  hydrogen  ion  and  at 
one  atmosphere  pressure  the  potential  developed  is  —0.27  volt.  For 
other  concentrations  the  potential  is,  of  course,  found  by  use  of  our  fun- 
damental equation,  thus:  P  =  -0.27+0.058  log  1/(H+). 

Being  only  one  element  out  of  a  "  couple,"  the  hydrogen  electrode 
must  be  used  along  with  some  other  combination  in  order  that  its  poten- 
tial may  be  measured.  For  this  purpose  the  calomel  electrode  is 
almost  the  universal  companion.  The  sketch,  Fig.  44  (which  is  purely 
diagrammatic),  will  serve  to  show  the  essential  arrangement  of  parts 
when  the  hydrogen  and  calomel  electrodes  are  thus  combined.  At  the 
right  is  the  calomel  electrode  with  its  constant  potential  of  —0.56  volt; 
at  the  left  is  the  hydrogen  electrode ;  and  connecting  the  two  electrodes 
is  the  solution  containing  the  hydrogen  ion. 


290 


ELECTROCHEMISTRY 


The  potential  of  the  above  combination,  as  in  any  primary  cell,  is  the 
algebraic  difference  between  the  two  electrode  potentials.     With  normal 


— -  4- 


FIG.  44.  —  Diagram  of  Arrangement  for  the  Hydrogen  Electrode. 

hydrogen  ion  the  potential  will  therefore  be  —0.27  —(  —  0.56),  or  0.29 
volt.     For  other  concentrations  we  have 

E.M.F.  =  -0.27+[0.058  log  1/(H+)]-  (-0.56) 
which  simplifies  to 

E.M.F.  =0.29+0.058  log  1/(H+).* 

But,  as  indicated  in  the  title  of  this  section,  the  hydrogen  electrode  is 
used  almost  exclusively  for  the  determination  of  hydrogen  ion  concen- 
tration. The  value  (H+)  therefore  becomes  our  unknown.  Solving 
for  this  we  have,  first 

,  //TT4,     E.M.F.  -0.29 
logl/(H  )=     ~ 


From  this  we  obtain  log  (H+)  and  then  (H+). 

The  following  example  will  make  the  calculation  clear: 

The  E.M.F.  measured  is  0.50  volt.     What  is  the  hydrogen  ion  con- 

centration, (H+)? 

Substituting  we  have 

0.50-0.29 


*  The  fact  that  the  E.M.F.  has  a  positive  value  means  simply  that  the  calomel 
electrode  becomes  the  positive  pole  of  the  couple;  that  is,  the  positive  current  comes 
from  the  calomel  electrode. 


DECOMPOSITION  VOLTAGE  291 

Log  1/(H+),  therefore,  equals  3.6207,  and  log  (H+)  =0.0000-3.6207 
=4.3793.*  From  this  (H+)  =  2.395 X10"4. 

It  is  becoming  customary  now  in  stating  H+  ion  concentration  to  use 
directly  the  values  for  log  1/(H+)  instead  of  the  numerical  values  for 
(H+).  Thus  stated,  the  values  are  designated  as  PH. 

The  E.M.F.  is  measured  by  what  is  termed  the  "  compensation 
method,"  balancing  against  a  standard  cell,  or  against  a  fraction  of  the 
voltage  of  an  ordinary  cell  measured  by  means  of  a  voltmeter.  The 
details  we  cannot  give  here,  f 

We  may  note  that  the  use  of  the  hydrogen  electrode  is  coming  into 
great  prominence  in  commercial  laboratories  for  electrometric  titration, 
and  in  biological  and  medical  laboratories  for  the  investigation  of  the 
blood  and  other  fluids. 

Decomposition  Voltage. — We  have  seen  how  the  potential  existing 
between  a  metal  and  its  ion  can  be  utilized  for  the  production  of  a 
current.  We  have  now  to  show  how  we  must  encounter  these  poten- 
tials if  we  try  to  force  the  ions  of  the  metals  out  of  solution,  as  we  do 
in  electrolysis.  We  have  noted  also  that  the  negative  ions,  such  as 
Cl~  and  OH~,  possess  similar  electrode  potentials,  and  we  shall  find 
that  these  too  must  be  encountered  in  the  same  way. 

We  can  see  at  once  that,  if  we  had  a  normal  solution  of  zinc  ion 
and  attempted  to  plate  the  metal  out,  we  should  have  to  work  against 
the  tendency  of  the  zinc  to  go  into,  or  remain  in,  the  ionic  condition. 
This  tendency  has  a  value  of  0.5  volt;  and  we  should  get  nothing  done 
until  we  applied  a  reverse  E.M.F.  of  a  little  more  than  this.  But  we 
cannot  electrolyze  a  solution  without  having  two  electrodes.  Suppose, 
then,  we  have  two  platinum  electrodes  dipping  into  a  solution  of  zinc 
sulphate,  and  should  then  attempt  to  electrolyze  the  solution.  So 
far  as  the  zinc  is  concerned  we  must  apply  an  E.M.F.  of  +0.5  volt. 
At  the  other  electrode  hydroxyl  ion  (possibly  864 =)  must  discharge 
and  then  react  to  produce  water  and  oxygen.  Now  the  discharging 
potential  of  OH~  in  normal  solution  is  —0.70,  but  in  this  solution  of 
zinc  sulphate,  where  the  OH  concentration  is  about  10~7,  its  dis- 
charging potential  is  about  ~1.85.  To  cause  the  discharge  of  this 
ion  we  must,  therefore,  apply  a  positive  E.M.F.  of  1.85  volts  in  the  same 
direction  as  in  the  case  of  the  zinc.  The  total  E.M.F.  necessary,  then, 
to  cause  the  continuous  electrolysis  of  zinc  sulphate  of  normal  ion  con- 
centration is  0.5+1.85,  or  2.35  volts. 

*  This  is  the  co-log  of  1/(H+). 

t  Further  details  concerning  the  theory  of  the  hydrogen  electrode  and  the  tech- 
nique of  its  use  may  be  found  in  the  following: 

(a)  Article  by  Joel  H.  Hildebrand,     Jour.  Am.  Chem.  Soc.,  35,  847. 

(6)  W.  M.  Clark,  The  Determination  of  Hydrogen  Ions  (1920). 


292  ELECTROCHEMISTRY 

What  is  true  of  zinc  sulphate  is  true  of  any  compound;  to  cause  con- 
tinuous electrolysis  we  must  overcome  the  electrode  potentials  of  the 
ions  by  impressing  a  counter  E.M.F.  of  a  little  more  than  equal  value. 
This  necessary  E.M.F.  is  called  the  "  decomposition  voltage  "  of  the 
given  electrolyte. 

We  have  seen  that,  when  we  electrolyze  any  acid  or  base  which 
gives  oxygen  at  the  anode  and  hydrogen  at  the  cathode  (e.g.,  H2SO4 
HNOs,  NaOH,  or  Ca(OH)2),  the  electrode  reactions  are  in  all  cases 
identical,  namely,  discharge  of  OH—  at  the  anode  and  discharge  of 
H+  at  the  cathode.  From  this  we  should  expect  the  decomposition 
potentials  of  all  such  compounds  to  be  the  same.  This  we  find  to  be 
true.  The  decomposition  potential  of  all  the  compounds  mentioned  is 
practically  1.67  volts  *  in  normal  ion  concentration. 

The  decomposition  voltages  for  the  halogen  acids  are  invariably 
lower  than  those  of  the  oxygen  acids,  except  at  very  great  dilution. 
This  is  exactly  what  would  be  expected,  for  in  these  cases  we  are  dealing 
with  the  discharge  of  the  halogen  ions,  whose  potentials  are  all  lower  than 
that  of  hydroxyl.  The  fact  that  at  great  dilution  the  values  approach 
those  of  the  oxygen  acids  is  also  explained  at  once  when  we  find  that 
under  these  conditions  oxygen  is  given  off,  indicating  that  OH~  is  being 
discharged  as  well  as  the  halogens. 

Decomposition  Voltage  and  Electrode  Material:  Overvoltage.— 
(a)  Where  the  electrodes  are  of  the  same  metal  as  that  represented  by 
the  ions  in  solution  no  decomposition  potential  ordinarily  exists,  unless, 
as  seen  in  the  concentration  cell,  the  concentrations  around  the  two 
electrodes  are  different.  An  example  is  the  copper  coulometer  where 
we  have  copper  plates  immersed  in  copper  sulphate  solution.  In  such  a 
cell  the  potential  developed  at  one  electrode  is  exactly  balanced  by  an 
oppositely  directed  potential  at  the  other,  and  the  application  of  the 
least  potential  in  either  direction  at  once  starts  the  electrolysis.  The 
use  of  a  cathode  of  some  other  material  will  in  no  wise  alter  the  situation, 
provided  only  that  it  is  a  good  conductor  and  that  the  copper  can  adhere 
to  it.  When  the  electrolysis  is  started  such  a  cathode  will  immediately 

*  In  an  acid  of  normal  ion  concentration  this  value  must  be  made  up  of  the 
normal  value  for  H+,  namely  ~0.27,  and  the  value  —1.94  for  the  OH~~,  the  alge- 
braic difference 'being  1.67.  This  seemingly  abnormal  value  for  the  OH~  is  due, 
no  doubt,  to  the  extremely  small  concentration  of  this  ion  found  in  the  presence 
of  a  high  concentration  of  H+.  In  an  alkali  of  normal  ion  concentration,  where 
OH~  has  a  potential  of  —0.70,  the  value  for  H+  must  be  +0.97,  the  high  value 
being  due,  as  in  the  case  of  OH~  above,  to  the  small  concentration  of  the  ion. 

For  fuller  discussion  of  this  matter  of  decomposition  voltage,  see  Le  Blanc, 
Electro-chemistry,  pp.  286-320  (1907),  and  Jones,  Physical  Chemistry,  pp.  482- 
491  (1907). 


DECOMPOSITION  VOLTAGE  293 

become  coated  with  copper,  and  will  then  be,  to  all  intents  and  pur- 
poses, a  copper  cathode. 

(b)  Where  hydrogen  is  the  cation  a  certain  amount  of  the  gas  is 
occluded  in  the  cathode,  and  the  back  pressure  (solution  pressure) 
exerted  by  the  gas  seems  to  be  inversely  proportional  to  the  amount  of 
this  occlusion.  Since  the  decomposition  potential  is  really  the  differ- 
ence between  the  solution  pressure  and  the  pressure  of  the  ion,  it  is 
evident  that  the  less  the  amount  of  occlusion,  the  greater  will  be  the 
positive  E.M.F.  of  the  hydrogen.  In  the  potential  series,  hydrogen  is 
given  a  value  of  —0.27.  This  value  was  obtained  by  use  of  the  "  hydro- 
gen electrode,"  which  is  really  hydrogen  gas  occluded  in  finely  divided 
platinum.  On  most  metals  the  value  would  approach  more  nearly 
zero  potential,  and  in  some  cases  would  even  have  a  positive  sign,  indi- 
cating that  the  solution  pressure  exceeds  the  pressure  of  the  normal  ion. 
The  following  table  gives  the  values  obtained  by  Caspari,*  for  the  elec- 
trode potentials  of  hydrogen  upon  several  different  metals: 

POTENTIAL  OF  HYDROGEN  ON  VARIOUS   METALS 

(Sign  of  Solution) 

H2  on  Hg +0.51 

H2  on  Zn +0.43 

H2  on  Pb +0.37 

H2  on  Sn +0.28 

H2on  Cu -0.04 

H2  on  Ni -0.06 

H2  on  Ag -0. 12 

H2  on  Pt  (smooth) -0. 18 

H2onFe -0.19 

H2  on  Pt  (black) -0.27 

Note  that  the  last  value  in  the  table  is  the  standard  potential  for 
hydrogen  as  obtained  by  the  use  of  a  platinum  black  electrode.  The 
difference  between  the  standard  value  and  the  value  observed  in  the 
case  of  any  metal  other  than  platinum  black  is  called  the  "  overvoltage  " 
of  hydrogen  for  the  given  metal. 

It  will  be  noted,  too,  that  this  difference  in  the  potential  of  hydrogen 
on  different  metals  causes  a  great  variation  in  the  position  of  hydrogen 
in  the  potential  series.  As  given  in  the  table,  hydrogen  (on  platinum 
black)  occupies  a  position  between  lead  and  copper.  On  mercury  its 
position  would  be  shifted  to  the  space  between  zinc  and  manganese. 
On  other  metals  it  would  occupy  various  other  positions  in  the  series. 

*  Zeitschr.  physikal.  chemie,  30,  89  (1899). 


294  ELECTROCHEMISTRY 

This  shifting  of  the  potential  of  hydrogen  alters,  of  course,  the  decom- 
position potential  of  any  electrolyte  which  gives  hydrogen  as  one  of  its 
products.     Thus,  while  on  platinum  black  electrodes  the  decomposition 
voltage  of  sulphuric  acid  is  —0.27— (—1.94),  or  1.67  volts,  on  a  mer 
cury  cathode  this  value  would  become  +0.51  — (  —  1.94),  or  2.45  volts. 

(c)  As  mentioned  above,  the  discharging  potential  of  the  anion  is 
also  affected  by  the  make-up  of  the  electrodes.  We  could  show  series 
of  overvoltages  here  also;  but  for  our  purpose  the  cathode  effect  is  much 
more  important,  so  we  shall  confine  our  application  to  that  side. 

Decomposition  Potential  in  Electro-analysis. — The  matter  of  decom- 
position potential  lies  at  the  bottom  of  nearly  all  the  separations  made  in 
electro-analysis.  Where  a  solution  contains  two  metal  ions  of  consider- 
ably different  decomposition  potential,  it  is  possible  to  apply  an  E.M.F. 
which  is  quite  sufficient  to  plate  out  one  metal  and  is  too  low  to  affect 
the  other.  It  should  be  remembered,  however,  that  the  potentials 
given  in  the  table  are  for  normal  ion  concentration;  and  as  a  metal  sep- 
arates and  the  ionic  osmotic  pressure  goes  lower  and  lower,  the  back 
E.M.F.  due  to  the  solution  pressure  more  and  more  preponderates  and 
increases  the  discharging  potential.  If  the  two  metals  lie  too  close  to- 
gether in  the  potential  series,  it  is  quite  possible  that  before  one  has 
been  entirely'  separated  the  voltage  required  may  begin  the  separation  of 
the  other.  The  easiest  separations  are  those  of  metals  which  lie  on 
opposite  sides  of  hydrogen.  The  element  lying  lowest  in  the  series, 
i.e.,  having  the  lowest  potential,  comes  out  first,  and  is  followed  by  the 
next  in  order,  which  in  such  cases  is  hydrogen.  There  is  no  danger  of 
separating  the  metal  of  higher  potential  so  long  as  enough  hydrogen  ion 
is  present,  unless  extremely  high  voltages  are  used. 

The  matter  of  overvoltage  must  also  be  considered  in  electro- 
analysis  along  with  ordinary  decomposition  potential,  as  the  following 
examples  will  show.  Neither  zinc  nor  iron  can  be  separated  quanti- 
tatively from  an  acid  solution  by  electrolysis  on  metal  plates,  because 
hydrogen,  having  a  lower  potential,  will  come  out  first,  and  continue 
to  do  so,  leaving  the  metallic  ions  in  solution.  If,  however,  a  mercury 
cathode  is  used,  overvoltage  brings  hydrogen  above  iron  and  even  above 
zinc,  so  that  with  a  rather  high  E.M.F.  both  these  metals  may  be 
brought  quantitatively  into  the  mercury  in  the  form  of  amalgams.  In  a 
slightly  alkaline  solution  and  with  sufficiently  high  voltage,  even  the 
alkali  metals  may  be  brought  down  quantitatively  by  use  of  the  mer- 
cury cathode.  In  this  case,  however,  another  factor  is  brought  into 
•  play;  the  hydrogen  ion  concentration  is  extremely  low,  so  that  even 
without  the  mercury  cathode  its  discharging  potential  would  be 
extremely  high. 


POLARIZATION  295 

Polarization. — The  matter  of  polarization  is,  as  we  shall  see,  rather 
closely  related  to  decomposition  voltage,  and  should  naturally  follow  it 
in  the  discussion.  If  we  electrolyze  sulphuric  acid  between  platinum 
plates,  and  after  a  time  turn  off  the  electrolyzing  current,  a  voltmeter 
properly  connected  with  the  cell  will  not  give  zero  reading,  but  will  show 
an  appreciable  E.M.F.  counter  to  the  original  current.  This  is  due  to 
the  gases  hydrogen  and  oxygen,  which  are  still  clinging  to  the  electrodes, 
and  which  tend  to  go  back  into  the  ionic  condition.  In  other  words,  we 
have  a  hydrogen-oxygen  cell  analogous  to  any  other  primary  cell.  The 
effect  of  this  polarization  due  to  the  electrolytic  gases  often  has  to  be 
taken  into  account.  Thus,  in  the  common  cell,  made  by  immersing 
strips  of  zinc  and  copper  in  dilute  sulphuric  acid,  we  have  zinc  going 
into  solution  and  hydrogen  coming  out  on  the  copper.  This  hydrogen 
causes  polarization  here  just  as  it  does  on  the  platinum,  and,  indeed, 
the  effect  is  somewhat  greater,  due  to  its  overvoltage  on  copper.  When 
the  plates  are  first  immersed  in  the  acid  and  before  hydrogen  collects 
on  the  copper,  the  E.M.F.  of  the  cell  is  about  1  volt,  but  after  a  current  is 
allowed  to  pass  for  a  few  minutes,  the  E.M.F.  will  be  seen  to  drop  to 
about  0'54  volt.  (Give  the  theoretical  E.M.F.  of  such  a  combination, 
taking  into  consideration  the  overvoltage.) 

Since  polarization  is  here  produced  by  the  accumulation  of  hydrogen 
on  the  cathode,  we  should  expect  to  be  able  to  overcome  it  by  preventing 
this  accumulation.  This  we  find  we  can  do  by  placing  in  contact  witli 
the  cathode  some  oxidizing  substance,  such  as  potassium  dichromate. 
Such  a  substance  is  called  a  "  depolarizer."  The  depolarizer  in  the 
"  dry  cell,"  is  manganese  dioxide.  Being  a  solid,  this -substance  cannot 
react  instantly;  therefore,  a  dry  cell  will  polarize  on  continued  use  in 
spite  of  it.  On  standing,  however,  the  cell  "  recovers." 

Displacement  of  Ions  by  Metals  and  Non-metals. — In  all  our  dis- 
cussion relating  to  the  source  of  chemical  E.M.F.,  we  have  considered 
only  those  cases  where  a  metal  was  brought  in  contact  with  a  solution 
containing  its  own  ion.  We  shall  now  show  what  will  result  when  a 
metal  or  a  non-metal  is  immersed  in  a  solution  containing  ions  of  other 
substances. 

When  a  strongly  positive  metal,  like  zinc,  is  brought  in  contact 
with  some  weakly  positive  ion,  like  copper,  the  latter,  as  is  well  known,  is 
immediately  displaced,  the  zinc  going  into  the  ionic  condition  and  the 
copper  coming  out  of  the  ionic  condition.  In  such  cases  the  reaction 
does  not  cease,  as  when  a  metal  is  brought  in  contact  with  its  own  ion, 
because  no  potential  is  developed.  What  actually  occurs  is  that  atoms 
of  zinc  give  up  the  necessary  electrons  to  the  copper,  becoming  zinc 
ions,  while  the  copper  ions  take  on  these  same  electrons  to  become 


296  ELECTROCHEMISTRY 

copper  atoms.  The  change  is  summed  up  in  the  following  reaction, 
which,  however,  does  not  show  the  transfer  of  electrons: 

Zn+Cu++  -»  Zn+++Cu 

The  reaction  occurs  because  the  zinc  has  a  much  higher  solution 
pressure  than  the  copper,  and  therefore  forces  upon  the  copper  the  elec- 
trons which  the  latter  is  only  too  willing  to  receive. 

Displacement,  then,  is  simply  a  matter  of  solution  pressure:  the 
higher  the  solution  pressure  of  an  element  the  greater  its  displacing 
power.  Now,  the  order  of  the  elements  in  our  table  of  potential  series 
is  also  a  matter  of  solution  pressure,  those  at  the  top  of  the  table  having 
high  solution  pressure  and  those  at  the  bottom  low  solution  pressure. 
We  may  therefore  expect  that  the  order  of  displacement  will  be  the  same 
as  the  order  in  the  potential  series.  This,  indeed,  we  do  find,  for  in 
general  a  metal  will  displace  any  positive  ion  which  lies  below  it  in  the 
series.  For  the  same  reason  a  non-metal  will  displace  any  negative  ion 
which  lies  below  it  in  the  series. 

Solution  of  a  metal  in  an  acid  means  simply  the  displacement  of 
hydrogen  ion  (except  in  the  case  of  nitric  acid,  which  is  a  matter  of 
oxidation)  and  should,  therefore,  follow  in  general  the  ordinary  rules  for 
displacement.  We  should,  for  example,  expect  any  metal  lying  above 
hydrogen  in  the  potential  series  to  "  dissolve  "  in  any  strong  (highly 
ionized)  acid.  But  we  note  at  once  that  this  displacement  of  hydrogen 
which  is  a  matter  of  solution  pressure,  involves  overvoltage,  which  is  also 
a  matter  of  solution  pressure.  Whether  a  given  metal  will  dissolve  in  an 
acid,  therefore,  depends  on  the  position  hydrogen  will  take  in  the  series 
when  displaced  on  the  surface  of  this  particular  metal.  For  example,  it 
is  an  observed  fact  that  pure  zinc  scarcely  dissolves  at  all  in  hydrochloric 
acid  of  normal  concentration.  This  is  instantly  explained  as  an  over- 
voltage  effect.  In  order  to  dissolve,  zinc  must  displace  hydrogen,  not 
on  platinum,  but  on  its  own  surface.  But,  according  to  the  overvoltage 
series,  hydrogen  on  zinc  has  a  potential  of  +0.43,  scarcely  lower  than 
that  of  zinc  itself  (+0.5).  Under  such  conditions  zinc  should  displace 
hydrogen  only  with  extreme  slowness. 

It  is  interesting  to  note  that  if  a  piece  of  zinc  thus  in  contact  with 
hydrochloric  acid  be  touched  beneath  the  surface  of  the  acid  with  a  strip 
of  platinum,  solution  immediately  proceeds  rapidly;  but  the  hydrogen 
is  now  evolved  on  the  surface  of  the  platinum  where  the  potential  is 
much  lower. 

Another  observed  fact  related  to  the  above  is  that  zinc  covered  with 
a  layer  of  mercury  (amalgamated)  does  not  dissolve  at  all  in  normaj 


DISPLACEMENT   OF  IONS  BY   METALS  AND  NON-METALS     297 

hydrochloric  acid.  This  is  also  instantly  explained  by  use  of  the  over- 
voltage  principle.  Hydrogen  on  the  surface  of  mercury  has  a  higher 
potential  than  zinc  and  therefore  is  not  displaced  by  it.  Here  again 
rapid  solution  of  the  zinc  may  be  brought  about  by  touching  the  amal- 
gamated zinc  beneath  the  surface  of  the  acid  with  some  metal  upon 
whose  surface  the  hydrogen  has  less  overvoltage  (iron,  for  example). 

Very  interesting  and  useful  results  may  sometimes  be  obtained  by 
proper  regulation  of  the  matter  of  displacement.  Suppose,  for  example, 
we  have  a  solution  containing  antimony  and  tin  in  acid  solution,  and  we 
place  in  the  solution  a  strip  of  iron.  We  should  possibly  expect  to  see 
both  the  metals  and  also  the  hydrogen  ion  displaced,  since  they  all  stand 
below  iron  in  the  potential  series;  but  what  actually  occurs  is  that  the 
antimony,  standing  lowest  in  the  series,  is  displaced  first.  When  the 
antimony  is  all  out  of  the  solution,  hydrogen  will  come  next,  and  indeed  a 
little  hydrogen  may  be  displaced  before  the  antimony  is  all  out,  if  its 
concentration  is  large.  But  the  important  thing  is  that  no  tin  at  all 
will  be  displaced  so  long  as  the  solution  remains  acid.  This  process  is 
quantitative  and  may  be  used  as  an  accurate  method  of  separating  tin 
and  antimony. 

The  converse  of  this  method  may  also  be  used.  If  we  have  the  tin 
and  antimony  as  metals,  we  may  treat  them  with  hydrochloric  acid. 
The  tin,  standing  above  hydrogen  in  solution  pressure,  will  displace  it 
and  go  into  solution,  leaving  the  antimony  untouched. 

We  notice,  of  course,  that  the  process  of  displacement  among  metals 
is  really  one  of  reduction,  and  it  happens  that  in  some  cases  the  process 
does  not  extend  to  the  complete  reduction  and  consequent  precipitation 
of  a  metal,  but  acts  only  to  reduce  its  valence.  Thus  we  know  that 
ferric  iron  in  passing  over  the  zinc  in  the  Jones  reductor  is  not  reduced 
to  metallic  iron,  but  only  to  the  ferrous  condition.  Whether  the  process 
extends  to  complete  reduction  or  only  to  partial  reduction  depends 
somewhat  on  the  interval  in  the  potential  series  between  the  reducing 
metal  and  the  one  to  be  reduced.  Iron,  for  example,  standing  only  a 
short  distance  above  tin,  reduces  it  only  to  the  stannous  condition, 
while  zinc,  standing  much  higher,  reduces  it  to  the  metal. 

Another  factor  which  in  a  measure  governs  the  extent  to  which  a 
metal  ion  will  be  reduced  is  its  position  with  reference  to  hydrogen. 
Hydrogen  ion  is  present  to  some  extent  in  every  solution,  and  in  some 
cases,  such  as  those  of  tin  and  iron,  it  is  present  in  considerable 
amounts,  because  of  hydrolysis.  It  may,  therefore,  often  be  easier  to 
displace  hydrogen  than  to  reduce  a  metallic  ion  to  the  metal.  This 
explains  why  zinc  does  not  reduce  iron  to  the  metal  and  why  iron  does 
not  reduce  tin  to  the  metal.  Zinc  displaces  hydrogen,  of  course,  but, 


298  ELECTROCHEMISTRY 

standing  so  far  above  tin,  it  is  able  not  only  to  do  this,  but  also  to  carry 
the  reduction  of  the  tin  to  completion. 

EXERCISES 

1.  Define  the  "  coulomb  "  in  chemical  terms;   in  C.  G.  S.  units. 

2.  Define  the  "  ampere." 

3.  Discuss  the  matter  of  magnetic  field  developed  around  a  conducting  wire,  and 
give  the  important  details  of  the  construction  of  an  ammeter  (two  types) . 

4.  What  is  "  resistance"?     Define  the  "  ohm." 

6.  How  does  resistance  vary  with  the  shape  of  the  conductor?  A  wire  1  meter 
long  and  1  mm.  in  diameter  has  a  resistance  of  0.8  ohm.  What  is  the  resistance  of  a 
wire  of  the  same  material  5  meters  long  and  3  mm.  in  diameter? 

6.  Define  specific  resistance.     The  resistance  of  a  wire  1  meter  long  and  1  mm.  in 
<;ross-section  is  1  ohm.     What  is  the  specific  resistance  of  the  same  materials? 

7.  What    is    "  conductivity"?     How   is   it   measured?     Specific    conductivity? 
What  is  the  specific  conductivity  of  the  wire  mentioned  in  problem  5? 

8.  Describe  "  Wheatstone's  bridge  "  and  show  how  resistance  is  measured  by  its 
use.     How  is  the  resistance  of  a  solution  measured? 

9.  Define  the  "  volt."     Describe  the  voltmeter. 

10.  Define  "  Ohm's  Law." 

11.  Draw  a  sketch  of  a  rheostat  and  describe  its  use. 

12.  Define  "  watt "  and  "  kilowatt."     What  current  passes  through  a  60-watt 
lamp  under  a  potential  of  110  volts? 

13.  A  motor  draws  a  current  of  0.5  ampere  under  a  potential  of  110  volts.     How 
much  does  it  cost  per  hour  to  run  it  at  the  rate  of  12  cents  per  kilowatt-hour? 

14.  What  relation  exists  between  wattage  and  candle-power  in  the  tungsten  and 
the  carbon  lamps? 

15.  What  is  an  electrical  horse-power?    What  is  the  horse-power  of  a  50-watt 
motor?  of  a  550-watt  flatiron? 

16.  State  and  illustrate  Faraday's  "  first  law." 

17.  State  Faraday's  "second  law."     If  a  certain  current  sets  free  1.25  gm.  of 
zinc,  what  weight  of  chlorine  and  potassium  would  be  set  free  by  the  same  current  in 
the  same  time? 

18.  Write  out  a  carefully  worded  summary,  covering  the  electronic  explanation  of 
Faraday's  laws. 

19.  If  one  atom  of  copper  carries  two  unit  charges  of  electricity  and  one  gram- 
atomic  weight  carries  two  faradays,  how  many  atoms  are  there  in  a  gram-atomic 
weight  of  copper? 

20.  What  kind  of  change  always  occurs  at  the  cathode  in  electrolysis?     Name 
and  illustrate  three  ways  in  which  this  change  may  occur? 

21.  What  kind  of  change  occurs  at  the  anode?     Name  and  illustrate  three  ways 
in  which  this  change  may  occur. 

22.  Illustrate  and  explain  certain  so-called  "  secondary  "  reactions  that  may  occur 
at  anode  and  cathode. 

23.  Give  a  simple  method,  based  on  the  electrode  reactions,  by  which  one  may 
identify  the  "  poles  "  of  a  battery. 

24.  Show  what  occurs  at  the  electrodes  when  a  current  is  passed  through  the 
following  solutions:  HC1  with  Pt  electrodes,  HC1  with  Cu  electrodes,  H2SO4  with  Pt 
electrodes,  Na2SO4  with  Pt  electrodes,  FeCls  with  Pt  electrodes. 


EXERCISES  299 

25.  Using  silver  nitrate  as  an  example,  give  a  clear  discussion  of  the  meaning  of 
"  transport  "  numbers.     Effect  of  dilution  and  temperature? 

26.  A  solution  of  copper  sulphate  was  electrolyzed  between  copper  electrodes, 
and  0.2294  gm.  of   copper  was  deposited.      Before  electrolysis  the  anode  solution 
contained  1.1950  gm.  of  copper  and  after  electrolysis  1.3600  gm.      Calculate  the 
transport  numbers  for  Cu++  and  SO4=. 

27.  Describe  a  method  by  which  the  absolute  migration  velocity  of  ions  may  be 
determined. 

28.  Devise  an  experiment  by  which  we  may  decide  whether  silver  forms  a  part 
of  the  anion  or  a  part  of  the  cation  of  a  complex  cyanide. 

29.  Define   "  specific  conductivity  "  and   "  molecular  conductivity,"   and  show 
how  each  is  designated. 

30.  The  specific  resistance  of  M/10  hydrochloric  acid  is  28.5  ohms.     Calculate 
KIO  and  MIO. 

31.  What  is  meant  by  "  molecular  conductivity  at  infinite  dilution"?     How 
designated?     How  determined? 

32.  MOO  for  HC1  is  377.     /*  is  301.     Calculate  the  degree  of  ionization  (a). 

33.  MOO  for  HC1  is  377-     The  transport  number  for  H  in  HC1  is  0.828.     Find  the 
value  of  MOO  for  H+  and  Cl~. 

34.  By  use  of  the  table  of  conductivities  for  the  single  ions,  calculate  the  value  of 
MOO  f°r  acetic  acid,  HC2H3O2.   Could  this  value  be  determined  by  the  ordinary  method? 
Why? 

35.  The  specific  conductivities  of  KBr  and  HgCl2  in  M/10  solution  are  0.0112  and 
0.00024  respectively.     Calculate  the  degree  of  ionization  in  each  case,  making  use  of 
the  table  mentioned  in  34. 

36.  Discuss  the  development  of  potential  between  a  metal  and  its  ion,  including 
also  the  matter  of  sign.     Give  the  same  for  a  non-metal. 

37.  Discuss  the  two  potential  series.     How  may  the  values  from  one  be  translated 
into  those  of  the  other. 

38.  Develop  the  equation 

0.058         1 
log- 


and  illustrate  its  use. 

39.  What  potential  would  be  developed  between  a  strip  of  copper  and  3  N  Cu++? 
Between  copper  and  0.0001  N  Cu++? 

40.  Describe  in  detail  the  theory  of  the  Daniell  cell. 

41.  WThat  would  be  the  potential  of  a  Daniell  cell  containing  0.001  N  copper  ion 
and  2  N  zinc  ion? 

42.  Draw  sketch,  and  give  a  careful  description  of  the  Weston  cell,  including  the 
theory  of  its  constant  voltage. 

43.  Calculate  the  voltage  of  a  Weston  cell  on  the  assumption  that  both  mercurous 
ion  and  cadmium  ion  are  of  5  N  concentration. 

44.  Give  the  theory  of  the  concentration  cell. 

45.  Describe  the  drop  electrode  and  the  calomel  electrode,  and  show  how  by  their 
use  the  single  potentials  are  determined. 

46.  A  copper  electrode  dipping  in  copper  ion  was  combined  with  a  calomel  elec- 
trode and  the  voltage  of  the  couple  taken.      Its  value  was  0.05,  the  copper  being 
positive.     What  was  the  electrode  potential  of  the  copper? 

47.  Outline  carefully  the  theory  of  the  hydrogen  electrode,  and  show  exactly  how 
it  is  used. 


300  ELECTROCHEMISTRY 

48.  The  observed   E.M.F.  of  a  hydrogen   electrode  combined  with  a  calomel 
electrode  is  0.625.     Calculate  the  concentration  of  hydrogen  ion. 

49.  What  is  decomposition  voltage?     Illustrate.     What  regularity  is  seen  in  the 
decomposition  voltage  of  acids  and  bases?    Explain. 

60.  Describe  carefully  the  overvoltage  effect  in  decomposition  voltage. 
51.  How  does  decomposition  voltage  enter  into  electro-analysis? 

62.  What  is  polarization?     Illustrate. 

63.  Give  the  theory  of  ionic  displacement  and  show  how  overvoltage  may  enter 
into  it. 

64.  Show  how  metals  may  be  separated  by  proper  regulation  of  displacement. 
55.  How  is  reduction  related  to  displacement?    Illustrate  by  use  of  the  Jones 

reductor. 


302 


LOGARITHMS. 


Natural 
Numbere.  1 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

PROPORTIONAL  PARTS. 

1 

9 

3 

4 

5 

G 

7 

8  9 

10 

0000 

0043 

0086 

0128 

0170 

0212 

0253 

0294 

0334 

0374 

4 

8 

1 

17 

21 

2529 

3337 

11 

0414 

0453 

0492 

0531 

0569 

0607 

0645 

0682 

0719 

0755 

4 

8 

1 

1 

IS 

2326 

3034 

12 

0792 

0828 

0864 

0899 

0934 

0969 

1004 

1038 

1072 

1106 

3 

7 

1 

14 

17 

2124 

28  31 

13 

1139 

1173 

1206 

1239 

1271 

1303 

1335 

1367 

1399 

1430 

3 

6 

1C 

1 

16 

1923 

2629 

14 

1461 

1492 

1523 

1553 

1584 

1614 

1644 

1673 

1703 

1732 

3 

G 

12 

15 

IS 

21 

2427 

15 

1761 

1790 

1818 

1847 

1875 

1903 

1931 

1959 

1987 

2014 

3 

G 

1 

14 

17 

20 

2225 

16 

2041 

2068 

2095 

2122 

2148 

2175 

2201 

2227 

2253 

2279 

3 

5 

1 

13 

16  18  21  24 

17 

2304 

2330 

2355 

2380 

2405 

2430 

2455 

2480 

2504 

2529 

2 

B 

7 

10 

12 

1517 

2022 

18 

2553 

2577 

2601 

2625 

2648 

2672 

2695 

2718 

2742 

2765 

2 

5 

7 

12 

14  16 

1921 

19 

2788 

2810 

2833 

2856 

2878 

2900 

2923 

2945 

2967 

2989 

2 

4 

7 

11 

13 

16 

1820 

20 

3010 

3032 

3054 

3075 

3096 

3118 

3139 

3160 

3181 

3201 

2 

4 

i 

11 

13 

15 

17  19 

21 

3222 

3243 

3263 

3284 

3304 

3324 

3345 

3365 

3385 

3404 

2 

4 

I 

10 

12  14 

16  18 

22 
23 

3424 
3617 

3444 
3636 

3464 
3655 

3483 
3674 

3502 
3692 

3522 
3711 

3541 
3729 

3560 
3747 

3579  3598 
3766,3784 

2 
2 

4 
4 

6 
( 

X 

10 
9 

12 
11 

14 
13 

15^17 
15  17 

24 

3802 

3820 

3838 

3856 

3874 

3892 

3909 

3927 

3945 

3962 

2 

4 

5 

7 

11 

12 

14  16 

25 

3979 

3997 

4014 

4031 

4048 

4065 

4082 

4099 

4116 

4133 

2 

3 

5 

7 

g 

10 

12 

1415 

26 

4150 

4166 

4183 

4200 

4216 

4232 

4249 

4265 

4281 

4298 

2 

3 

5 

7 

8 

1011 

13  15 

27 

4314 

4330 

4346 

4362 

4378 

4393 

4409 

4425 

4440 

4456 

2 

3 

5 

G 

8 

9 

11 

13  14 

28 

4472 

4487 

4502 

4518 

4533 

4548 

4564 

4579 

4594  4609 

2 

3 

5 

6 

8 

9 

11 

12  14 

29 

4624 

4639 

4654 

4669 

4683 

4698 

4713 

4728 

4742 

4757 

1 

3 

4 

6 

7 

9 

10 

12  13 

30 

4771 

4786 

4800 

481* 

4829 

4843 

4857 

\ 
4871 

4886 

4900 

1 

3 

4 

6 

7 

9 

10 

11  13 

31 

4914 

4928 

4942 

4955 

4969 

4983 

4997 

5011 

5024 

5038 

1 

3 

4 

G 

7 

8 

10 

11  12 

32 

5051 

5065 

5079 

50925105 

5119 

5132 

5145 

515$ 

5172 

1 

3 

4 

5 

7 

8 

9 

11  12 

33 

5185 

5198 

5211 

5224  5237 

5250 

5263 

5276 

5289 

5302 

1 

3 

4 

5 

6 

8 

9  10  12 

34 

5315 

5328 

5340 

5353 

5366 

5378 

5391 

5403 

5416 

5428 

1 

3 

^ 

5 

6 

8 

9 

1011 

35 

5441 

5453 

5465 

5478 

5490 

5502 

5514 

5527 

5539 

5551 

1 

2 

4 

f- 

6 

9 

1011 

36 

5563 

5575 

5587 

5599 

5611 

5623 

5635 

5647 

5658 

5670 

1 

2 

4 

PJ 

6 

5 

1011 

37 

56^2 

5694 

5705 

5717 

5729 

5740 

5752 

5763 

5775 

£786 

1 

2 

5 

6 

8 

9  10 

38 

5798 

5809 

5821 

5832 

5843 

5855 

5866 

5877 

5888 

5899 

1 

2 

1 

G 

6 

$ 

910 

39 

5911 

5922 

5933 

5944 

5955 

5966 

5977 

5988 

5999 

6010 

1 

2 

4 

8 

910 

40 

6021 

6031 

6042 

6053 

6064 

6075 

6085 

6096 

6107 

6117 

1 

2 

4 

6 

8 

910 

41 

6128 

6138 

6149 

6160 

6170 

6180 

6191 

6201 

6212 

6222 

1 

2 

4 

6 

7 

8  9 

42 

6232 

6243 

6253 

6263 

6274 

6284 

6294 

6304 

6314 

6325 

1 

2 

4 

6 

8  9 

43 

6335 

6345 

6355 

6365 

6375 

6385 

6395 

6405 

6415 

6425 

1 

2 

4 

6 

8  9 

44 

6435 

6444 

6454 

6464 

6474 

6484 

6493 

6503 

6513 

6522 

I 

2 

4 

6 

8  9 

45 

6532 

6542 

6551 

6561 

6571 

6580 

6590 

6599 

6609 

6618 

1 

2 

4 

6 

8  9 

46 

6628 

6637 

6646 

6656 

6665 

6675 

6684 

6693 

6702 

6712 

2 

^ 

6 

7  8 

47 

6721 

6730 

6739 

6749 

6758 

6767 

6776 

6785 

6794 

6803 

2 

4 

5 

6 

7  S 

48 

6812 

6821 

6830 

6839 

6848 

6857 

6866 

6875 

6884 

6893 

2 

4 

4 

E 

G 

7  3 

49 

6902 

6911 

6920 

6928 

6937 

6946 

6955 

6964 

6972 

6981 

2 

4 

4 

5 

6 

7  3 

50 

6990 

6998 

7007 

7016 

7024 

7033 

7042 

7050 

7059 

7067 

2 

3 

3 

4 

5 

6 

7  3 

51 

7076 

7084 

7093 

7101 

7110 

7118 

7126 

7135 

7143 

7152 

2 

3 

3 

4 

5 

6 

7  8 

52 

^160 

7168 

7177 

7185 

7193 

7202 

7210 

7218 

7226 

7235 

2 

2 

3 

4 

5 

6 

7  > 

53 

7243 

7251 

7259 

7267 

7275 

7284 

7292 

7300 

7308 

7316 

2 

2 

3 

4 

5 

6 

6  ? 

54 

7324 

7332 

7340 

7348 

7356 

7364 

7372 

7380 

7388 

7396 

1 

2 

2 

3 

4 

5 

6 

6  7 

LOGARITHMS. 


303 


[  Natural 
Numbers.  1 

0 

1 

2 

3 

4 

5 

G 

7 

8 

9 

PROPORTIONAL  PARTS. 

1 

2 

3 

4 

/> 

6 

7 

8 

6 

55 

7404 

7412  7419 

7427 

7435 

7443  7451 

7459 

7466  7474 

1 

Q 

fl 

3 

4 

5 

5 

6 

7 

56 
57 

7482 
755S 

7490  7497 
7566  7574 

7505 

7582 

7513 
7589 

7520  7528 
7597  7604 

7536  7543  7551 
761276197627 

1 

1 

2 

2 

2 
2 

3 
3 

4 
4 

5 
5 

5 
5 

6 
6 

7 
7 

58 

7G34 

7642  7649 

7657 

7664 

7672 

7679  7686 

7694  7701 

1 

2 

3 

4 

4 

5 

6 

7 

59 

7709 

7716 

7723 

7731 

7738 

7745 

7752 

7760 

7767 

7774 

1 

2 

3 

4 

4 

5 

6 

7 

60 
61 

7782 
7853 

7789 
7860 

7796 

7868 

7803 

7875 

7810 

7882 

7818 
7889 

7825 
7893 

7832 
7903 

7839 
7910 

7846 
7917 

1 
1 

2 

2 

3 
3 

4 

4 

4 

4 

5 

5 

6 

o 

6 
6 

62 

7924 

7931 

7938 

7945 

7952 

7959 

7966 

7973 

7980 

7987 

1 

2 

3 

3 

4 

5 

6 

6 

63 

7993 

8000 

8007  8014 

8021 

8028 

8035  8041 

8048 

8055 

1 

2 

3 

3 

4 

5 

5 

6 

64 

8062 

8069 

8075 

8082 

8089 

8096 

8102  8109 

8116 

8122 

1 

2 

3 

3 

4 

5 

5 

6 

65 

8jt2» 

S136 

8142 

8149 

8156 

8162  8169  8176 

8182 

8189 

1 

2 

3 

3 

4 

5 

5 

6 

66 

<l  95  8202 

8209 

8215 

8222 

82288235824182488254 

1 

2 

3 

3 

4 

5 

5 

6 

67 

8261  8267 

8274 

8280 

8287 

8293  8299  8306  8312  8319 

1 

2 

3 

3 

4 

5 

5 

6 

68 

8325 

8331 

8338 

8344 

8351 

8357  8363  8370  8376  8382 

1 

2 

3 

3 

4 

4 

5  6 

69 

8388 

8395 

8401 

8407 

8414 

8420 

8426 

8432 

8439 

8445 

1 

2 

2 

3 

4 

4 

5 

6 

70 

8451 

8457 

8463 

8470 

8476 

8482 

8488 

8494 

8500 

8506 

1 

2 

2 

3 

4 

4 

5 

6 

71 

8513 

8519  8525 

8531 

8537 

8543  8549  8555  8561 

8567 

1 

2 

2 

3 

4 

4 

5 

5 

72 

»70 

8573 

cnqq 

8579  8585 

CAQQ  Qfi/f  K 

8591 

QfiCI 

8597 
86^7 

8603  8609  8615  8621  8627 

8663  SfifiQl»A'7£'»fi«l  Sfi«A 

1 

2 

2 

3 

4 

4 

5 

5 

rO 

74 

oOoo 

8692 

oooy 
8698 

<j\j-r*j 
8704 

ouox 

8710 

OUOl 

8716 

OUUO  OUUi7| 

8722  8727 

t~j\j  t  «_/ 

8733 

^J\J^J  A 

8739 

\J\J\-r\J 

8745 

1 

2 

2 

3 

4 

4 

5 

5 

75 

751 

8756 

8762 

8768 

8774 

8779 

87858791 

8797 

8802 

1 

2 

2 

3 

3 

4 

5 

5 

76 

808 

8814 

8820 

8825 

8831 

8837 

88428843 

8854  8859 

1 

2 

2 

3 

3 

4 

5 

5 

77 

865 

8871 

8876 

8882 

8887 

8893 

8899  8904 

8910,8915 

1 

2 

2 

3 

3 

4 

4 

5 

78 

921 

8927 

8932 

8938 

8943 

8949 

8954  8960 

8965  8971 

1 

2 

2 

3 

3 

4 

4 

5 

79 

976 

8982 

8987 

8993 

8998 

9004 

9009  9015 

9020 

9025 

1 

2 

2 

3 

3 

4 

4 

5 

80 
81 

031 

085 

9036 
9090 

9042 
9096 

9047  9053 
9101  9106 

9058 
9112 

9063  9069 
91179122 

90749079 
9128  9133 

1 
1 

2 
2 

2 
2 

3 
3 

3 
3 

4 
4 

4 
4 

5 

5 

82 

138 

9143 

9149 

9154  9159 

916591709175 

91S09186 

1 

1 

2 

2 

3 

3 

4 

4 

5 

83 

191 

9196 

9201 

9206  9212 

9217  9222  9227 

9232  9238 

1 

1 

2 

2 

3 

3 

4 

4 

5 

84 

243 

9248 

9253 

9258 

9263 

9269  9274  9279 

9234 

9289 

1 

1 

2 

2 

3 

3 

4 

4 

5 

85 

294 

9299 

9304 

9309 

9315 

9320 

9325  9330 

93359340 

1 

1 

2 

2 

3 

3 

4 

4 

5 

86 

345 

9350 

9355 

9360 

9365 

9370 

9375  9380 

9385  9390 

1 

1 

2 

2 

3 

3 

4 

4 

5 

87 

395 

9400 

9405  9410 

9415 

9420  9425  9430  9435  9440 

0 

1 

1 

2 

2 

3 

3 

4 

4 

88 

445 

9450 

94559460 

9465 

9469  9474  9479  9434  9489 

0 

1 

1 

2 

2 

3 

3 

4 

4 

89 

494 

9499 

9504 

9509 

9513 

9518 

9523 

9528 

9533 

9538 

0 

1 

1 

2 

2 

3 

3 

4 

4 

90 

542 

9547 

9552 

9557 

9562 

9566 

9571 

9576 

9531 

9586 

0 

1 

1 

2 

2 

3 

3 

4 

4 

91 

9590 

9595  9600  9605 

9609 

9614 

9619 

9624 

9628 

9633 

0 

1 

1 

2 

2 

3 

3 

4 

4 

92 

963" 

9643  9647,9652 

9657 

9661 

9666 

9671 

9675 

9680 

0 

1 

1 

2 

2 

3 

3 

4 

4 

93 

9685 

9689  9694  9699  9703 

970S 

9713  9717 

9722 

9727 

0 

1 

1 

2 

2 

3 

3 

4 

4 

94 

9731 

9736  '9741 

9745 

9750 

9754 

9759 

9763 

9768 

9773 

0 

1 

1 

2 

2 

3 

3 

4 

4 

95 

9777 

9782 

9786 

97919795 

9800 

9805  9809  9814 

9818 

0 

1 

1 

2 

2 

3 

3 

4 

4 

96 

9823 

9827  9832  9836  9841 

9845,9850  9854  9859 

9863 

0 

1 

1 

2 

2 

3 

3 

4 

4 

97 

98 
99 

9868 
9912 
9956 

9872  9877  9881  9886 
9917  9921  9926  9930 
9961  9965  9969j9974 

9890,9894 
9934  9939 
9978  9983 

9899 
9943 
9987 

9903 
9948 
9991 

9908 
9952 
0996 

0 
0 
0 

1 

1 
1 

1 
1 
1 

2 
9 
2 

2 
2 
2 

3 

3 
3 

3 
3 
3 

4 
4 
3 

4 
4 

4 

INDEX 


Abegg,  78 
Abegg's  rule,  78,  94 
Absolute  temperature,  17 
weights  of  molecules,  41 
Acetic  acid,  equilibrium    relations,    206, 

209,  213 
Acid  and  base-forming  nature,  95 

constant  boiling,  145 
Acids,  ionization  of,  177 
Alloys,  242 
a  particles,  scattering,  124 

track  of,  114 
a-ray  product,  117,  121 
a  rays,  112 

Aluminum    hydroxide,    amphoteric   na- 
ture, 259 
Ammeter,  264 
Ammonia  complexes,  254 
Ammonium  hydroxide  in  precipitation, 

259 

Ampere,  203 

Amphoteric  substances,  258 
Amphoterism,  a  periodic  function,  258 
Anode  rays,  107 
Argon  atom,  175 
Arrhenius,  169 

theory  of  ionization,  169 
Arsenious  oxide  as  a  reducing  agent,  85 
Association  of  water,  31 
Atomic  hypothesis,  55 
numbers,  91,  124 
shells,  126,  127 
structure,  123 

papers  on,  138 
volume,  96 
weights,  56 
exact,  61 

from  molecular  weights,  58 
from  specific  heats,  60 
present  day  work  on,  63 
table  of,  64 


Avogadro,  6,  39 
Avogadro's  law,  39 
deviations  from,  40 

Bases,  ionization,  177 

Becquerel,  112 

Berthollet,  46 

Berzelius,  50 

Berzelius'  atomic  weights,  58 

Bingham,  10 

Bodenstein,  200 

Bohr,  125 

Bohr's  theory  of  atomic  structure,  125 

Boiling-point,  26 

rise,  159 

Bonds,  valence,  74 
Boyle's  law,  12 

and  the  kinetic  equation,  15 

deviations  from,  12 
Buffer  solutions,  225 
/3  rays,  113 

/3-ray  products,  117,  121 
Bromine,  amphoteric  nature,  260 
Brownian  movement,  3 
Brown,  3 

Calcium  chloride,  233 

Calculations,  chemical,  69 

Calomel  electrode,  288 

Cannizzaro,  59 

Cannizzaro's  method  for  atomic  weights, 

59 

Carbon  atom,  132 
Carbonic  acid,  ionization,  193 

in  precipitation,  251 
Case  hardening,  148 
Cathode  rays,  107 
Change  of  state,  25 
Charles,  17 
Charles'  law,  17 

and  the  absolute  temperature,  17 


305 


306 


INDEX 


Chemical  combination,  Lewis-Langmuir 

theory,  129 
Chemical  tests,  182 
Chlorine,  isotopes  of,  48 
Chromium,  hexavalent,  259 

hydroxide,  259 
Classification  of  elements,  88 
Clausius,  168 
Combination,  laws  of,  46 
Combined  gas  law,  18 
Combining  volumes,  52 

and  multiple  proportions,  53 
Combining  weights,  49 
Common-ion  effect,  212 

in  titration,  217 
Complex  ammonia  compounds,  254 

equilibrium,  245 

cyanides,  256 

ions,  migration  of,  276 
in  precipitation,  254 

oxalates,  257 

tartrates  and  lactates,  257 
Component,  238 
Concentration  cell,  287 

of  ions,  179,  208 

molar,  151 

normal,  152 
Condensation,  heat  of,  31 

of  a  saturated  vapor,  33 

of  a  gas,  33 
Conductivity,  277 

and  dilution,  277 

and  ionization,  278 

molecular,  277 

of  single  ions,  278 

specific,  277 

Constant-boiling  acid,  145 
Constant  composition,  46 

H+  and  OH~  concentration,  225 
Constant,  equilibrium,  200 
Cooling  effect  of  evaporation,  30 
Coordination  numbers,  79 
Copper  sulphate,  vapor  pressure,  231,233 
Coulomb,  263 

Critical  temperature  and  pressure,  34 
Crookes,  106 
Crookes'  tubes,  106 
Crystal  structure,  10 
Curie,  Madame,  112 
Cyanide  complexes,  256 


Dalton,  55 

Dalton's  atomic  weights,  57 

hypothesis,  55 

and  the  laws  of  combination,  56 

postulates,  55 
Daniell  cell,  284 
d' Arson val  galvanometer,  264 
Davy,  166 
Decomposition  voltage,  291 

in  electro  analysis,  294 
Definite  proportions,  46 
Degrees  of  freedom,  238 
Deposits,  radioactive,  116 
Depression  of  freezing-point,  156 
Desiccation  by  use  of  hydrates,  233 
Dew  point,  28 
Dielectric,  173 

theory  of  ionization,  173 
Diffusion  of  gases,  20 
Dihydrol,  31 

Disintegration  hypothesis,  116 
Displacement  and  overvoltage,  296 

as  reduction,  297 

of  ions,  295 

selective,  297 

Dissociation,  electrolytic,  166 
Distribution  of  electrons,  table,  128 
Doebereiner,  88 
Doebereiner's  triads,  88 
Drop  electrode,  288 
Dumas,  43 
Dumas'  method  for  molecular  weights, 

43 
Dulong,  61 

and  Petit's  specific  heat  method,  61 

Electrical  units,  263 
Electrochemistry,  263 
Electrode  reactions,  271 
Electrolysis,  laws  of,  268 

nomenclature,  167 
Electromotive  force,  266 

and  concentration,  283 

chemical,  280 
Electronic  charge,  determination,  111 

conception  of  valence,  138 
Electrons,  107 

and  electric  currents,  109 

and  inductive  charges,  109 

and  lightning,  109 


INDEX 


307 


Electrons,  distribution  of,  128 

sharing,  129 

transference,  129 
Emanations,  radioactive,  114 
End  product,  radioactive,  120 
Equations,  68 

making  of,  68 

molecular,  68 

significance,  68 
Equilibrium,  definitions,  196 

and  concentration,  203 

and  pressure,  202 

and  temperature,  201 

complex,  245 

constants,  200 

effect  of  a  catalyst,  204 

heterogeneous,  228 

homogeneous,  196 

importance  of,  196 

ionic,  205 

kinetic  explanation,  197 
Equipartition  of  energy,  3 
Equivalent  weights,  50 

determination,  51 

of  oxidizing  and  reducing  agents,  83 

standard  for,  50 
Ethylene,  14 
Eutectic  alloys,  242 
Evaporation,  heat  of,  31 

cooling  effect,  30 

Faraday,  166 

Faraday's  laws,  basis  for,  270 

of  electrolysis,  268 
Fehling's  solution,  255 
Fluorine  atom,  134 
Fog  tracks  of  a.  particles,  114 
Formulas,  66 

making  of,  66 

significance,  66 

structural,  73 
Frazer,  163 
Free  path,  7 

Freezing-point  depression,  156 
Fusion,  29 
Fusion,  heat  of,  32 

Galvanometer,  d'Arsonval,  264 
7  rays,  114 
Gaseous  diffusion,  20 


Gases,  liquefaction,  35 

mean  free  path,  7 

pressure  of,  3 

temperature  effects,  16 
Gas-law  equation,  molecular,  20 
Gas  laws,  12 

combined,  18 
Gay-Lussac,  17 
Graham,  21 
Graham's  law,  21 

and  molecular  weights,  22 
Gram-equivalent  weights,  51 

-molecular  weights,  42 
Grotthus,  166 
Group  1,  97 

2,  99 

3,  100 

4,  100 

5,  101 

6,  101 

7,  102 

8,  102 
relations,  97 

Guldberg  and  Waage,  197 

Half  periods,  116,  120 
Halogens,  amphoteric  nature,  260 
Harkins,  48 

Harkins'  periodic  arrangement,  104 
Heat  and  molecular  motion,  3 

of  condensation,  32 

of  evaporation,  31 

of  fusion,  32 

of  neutralization,  83 
Helium  atom,  131 
Hertz,  107 

Heterogeneous  equilibrium,  228 
Hittorf,  167,  224 
Holland,  163 

Homogeneous  equilibrium,  196 
Horse-power,  electrical,  268 
Humidity  and  dew  point,  28 
Hydrates  of  calcium  chloride,  233 

of  cupric  sulphate,  231 

vapor  pressure  of,  230 
Hydriodic  acid,  equilibrium  constant,  200 
Hydrogen  atom  and  molecule,  131 

electrode,  289 

ion  concentration,  determination,  290 

ion,  migration,  276 


308 


INDEX 


Hydrogen  overvoltage,  292 
potential  on  various  metals,  293 
sulphide  as  reducing  agent,  85 
sulphide  in  precipitation,  252 

Hydrolysis  of  salts,  220 
degree  of,  222 
of  NaCl  and  NaNO3,  220 
of  KCN  and  Na2CO3,  221 
of  NH4C1,  222 
of  NH4CN  and  (NH4)2CO2,  222 

Hydrosulphuric  acid,  85,  252 

Indicators,  187 

choice  of,  191 

color,  188 

color  range,  189 

determination  of  end  point,  190 

end  point,  188 

end-point  correction,  192 

table  of,  189 
Ion  concentration,  calculation  of,  179 

from  equilibrium  constants,  208 
Ionic  charge,  172 

equilibrium,  205 

displacement,  212 
lonizable  substances,  170 
lonization  and  catalysis,  183 

and  chemical  activity,  181 

and  chemical  tests,  182 

and  conductivity,  278 

cause  of,  171 

constants,  205 
from  hydrolysis  data,  224 
table  of,  208 

degree  of,  175 

function  of  solvent,  172 

of  acids,  177 

of  bases,  177 

of  organic  substances,  182 

of  poly  basic  acids,  180 

of  salts,  178 

of  strong,  electrolytes,  211 

of  water,  178 

theory  of,  166 
Ions,  170 

changes  of,  172 

migration  of,  273 
Iron,  amphoteric  nature,  260 

case  hardened,  148 
Isotopes  and  constant  composition,  47 


Isotopic  forms  of  lead,  47 

of  chlorine,  48 
Isosterism,  137 

Joule,  36 
Joule-Thomson  effect,  36 

Kahlenberg,  182 
Kelvin,  Lord,  36 
Kilowatt,  267 
Kinetic  energy,  3 
of  molecules,  3 

equation,  15 

theory,  1 
Kohlrausch,  167 

Lactates,  complex,  257 
Langmuir,  126 

Langmuir's  postulates,  126,  129 
Laws  of  combination,  46 
Lead,  end  product,  118,  120 

isotopes  of,  47,  120 
Le  Chatelier's  theorem,  202 
Lenard,  107 
Lewis,  126 

Life  periods,  116,  120 
Linde's  liquefaction  apparatus,  36 
Liquefaction  of  gases,  35 
Liquids,  associated,  8 

definition,  8 

kinetic  properties,  8 

solubility,  143 

structure,  8 

surface  tension,  8 
Lithium,  97,  98 

atom,  131 

Mean  free  path,  7 
Melting-point,  29 

and  pressure,  29 
Mendeleeff,  90 
Meyer,  Lothar,  90 
Migration  of  hydrogen  ion,  276 

of  ions,  273 
Millikan,  1,  108 

and  the  electronic  charge,  111 
Moh,  265 
Molar  concentration,  151 

volume,  42 

weights,  42 


INDEX 


309 


Mole,  20,  42 

Molecular  conductivity,  277 

equations,  68 

gas-law  equation,  20 

lowering  of  freezing-point,  157 

structure  of  matter,  1 

weights,  40 

determination,  43 
by  the  freezing-point  method,  158 
from  gaseous  diffusion,  22 
from  osmotic  pressure,  164 
Molecules,  absolute  weights,  41 

attraction  of,  8 

elasticity,  4 

kinetic  energy,  3 

motion,  3 

number,  4 

size,  6 

spacing,  4 

speed,  4 

Mono-hydrol,  31 
Morley,  50 
Morse,  163 
Moseley,  124 
Multiple  proportions,  51 

Neon,  135 
Neutralization,  215 

effect,  214 

heat  of,  183 
Newlands,  89 
Newlands'  octaves,  89 
Niton,  115 
Nitric  acid,  amphoteric  nature,  261 

as  an  oxidizing  agent,  83 
Nitrogen,  and  Boyle's  law,  14 

molecule,  136 
Non-polar  compounds,  130 
Normal  cadmium  cell,  286 

concentration,  152 
Nucleus,  atomic,  123 

Octet  theory  of  valence,  130 
Ohm,  264 
Ohm's  law,  266    • 
Osmotic  pressure,  160 

and  molecular  weights,  164 

cause,  161 

recent  work  on,  163 
Qxalates,  complex,  257 


Oxidation  and  reduction,  81 

electrical,  271,  272 
Oxidizing  agent,  82 
Overvoltage  of  hydrogen,  292 
Oxygen  atom  and  molecule,  133 
Ozone  molecule,  134 

Para  nitrophenol,  187 
Partial  pressures,  16 
Partition,  229 

of  bromine,  229 

of  succinic  acid,  229 
Periodic  arrangement,  90 

functions,  94 

system,  88 

table,  92 

Periods,  radioactive,  116,  120 
Perrin,  3,  107 
Petit,  61 
Pfeffer,  160 
Phase,  238 
Phase  rule,  237 

applications,  239 
Phosphoric  acid,  titration,  193 
Planetary  system,  125 
Plumber's  solder,  phase  relations,  243 
Polar  compounds,  129 
Polarization,  295 
Polonium,  112,  120 
Polybasic  acids,  ionization  of,  180 

titration,  192 

Positive  and  negative  valence,  75 
Potassium  atom,  135 

dichromate  as  an  oxidizing  agent,  84 

permanganate  as  an  oxidizing  agent,  84 

amphoteric  nature,  261 
Potential,  definition  of,  266 

electrical,  266 

series,  table,  282 
Power,  electrical,  267 
Precipitates,  solution  of,  249 
Precipitation  by  weak  acids  and  their 
salts,  251 

theory  of,  248 
Prediction  of  properties,  103 
Pressure  of  gases,  3 
Pressure-volume  curve,  241 
Primary  cell,  284 
Proust,  46 
Prout,  88 


310 


INDEX 


Front's  hypothesis,  88 
Quantity,  electrical,  263 

Radioactive  elements,  discovery,  112 

rays  from,  17.2 

series,  118,  119 
Radium,  112 

emanations,  115 
Ramsay,  115 
Rayleigh,  Lord,  1 
Rays,  vacuum-tube,  106 
Reciprocal  proportions,  49 
Reducing  agent,  82 

valence,  82 
Resistance,  electrical,  264 

specific,  265 
Rheostat,  267 
Richards,  10,  47 
Richter,  50 
Roentgen,  106 
Rutherford,  113 

Salt  effect,  174 

Salts,  ionization  of,  178 

Saturated  solution,  141 

vapor,  33 

Sharing  of  electrons,  129 
Silver  acetate,  precipitation,  248 

solution,  249 
Smale,  174 
Sodium  atom,  135 

thiosulphate,  86 
Soddy,  48 

Soddy's  periodic  arrangement,  104 
Solder,  phase  relations,  243 
Solid  solutions,  147 
Solubility,  142 

and  temperature,  144 

curves,  146 

of  fine  powders,  144 

of  gases,  142 

of  liquids,  143 

statement  of,  142 

product,  245 

calculation  of,  247 
effect  of  foreign  salts,  247 
Solution,  mechanism  of,  141 

of  precipitates,  249 
Solutions,  solid,  147 


Specific  conductivity,  277 

heats,  61 

resistance,  265 
Spinthariscope,  113 
Stas,  46,  50 

Steel,  a  solid  solution,  148,  151 
Stoney,  107 

Strong  electrolytes,  ionization,  211 
Structural  formulas,  73 
Structure,  atomic,  123 
Sublimation,  30 
Superheating,  26 
Supersaturated  solutions,  150 
Supersaturation,  148 
Symbols,  66 

Tartrates,  complex,  257 
Temperature,  absolute,  18 

effects  with  gases,  16 
Tetrahedral  carbon  atom,  133 
Theory  of  ionization,  166 

of  precipitation,  248 
Thomson,  J.  J.,  107 
Thomson  (Lord  Kelvin),  36 
Thorium  series,  119 
Time-temperature  curve,  240 
Transference  combination,  129 
Transport  numbers,  276 
Traube,  160 
Tri-hydrol,  31 

Uranium  series,  118 

Valence,  72 
a  periodic  function,  94 
and  structural  formulas,  73 
change  of,  81 
electronic  conception,  138 
idea  of,  72 

Langmuir's  equation,  130 
octet  theory,  130 
oxidation  and  reduction,  81 
positive  and  negative,  75 
primary  and  secondary,  79 
saturated  and  unsaturated,  78 
variability,  73 

Van  der  Waals,  13 

Van  der  Waals'  equation,  13 

Van't  Hoff,  162 

Van't  Hoff's  generalization,  162 


INDEX 


311 


Van't  Hoff  on  ionization,  168 
Vapor,  condensation  of,  33 
pressure  a  function  of  temperature,  25 
of  water,  table,  26 
and  boiling-point,  26 
of  hydrates,  230 
saturated,  25,  33 
Victor  Meyer,  44 
Volt,  266 

Walden,  172 

Water,  amphoteric  nature,  258 

constant  for,  218 

ionization  of,  178 


Water,  phase  relations  of,  235 

Watt,  267 

Werner,  79 

Weston  cell,  286 

Wheatstone's  bridge,  265 

Wilson,  113 

Work,  electrical,  267 

X-ray  spectra  and  nuclear  charge,  124 

tube,  106 
X-rays,  108 

Zero  group,  97 


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